Normal mode analysis of pair plasma with drifting species
Pair-ion plasmas consisting of C60+ and C60- ions have been generated in laboratory using fullerene as an ion source1,2. In addition, electron-positron plasmas are believed to be abundant in many astrophysical environments from pulsars to quasars3,4. In laboratory also, electron-positron pair plasma has been generated with the help of ultraintense lasers5 and by trapping of positron in a magnetic mirror configuration by electron cyclotron resonance heating6. Since plasmas are nonlinear and dispersive media, it would be very much interesting to examine whether such pair-plasmas support the excitation of solitary waves and solitons. This has motivated us to do analytical calculations for studying the modes of solitary wave propagation. One-dimensional two-fluid plasma having streaming positrons and electrons is studied through normal mode analysis. We analyze how many types of modes propagate in these plasmas and also compare our results with previously explored models by other researchers. We obtained the dispersion relation and solved for the phase velocity of the acoustic modes. Although the dispersion relation predicts four types of the modes, only two types of the modes (namely fast and slow mode) are possible in the present plasma model. We find all the roots to be real. Therefore, it may be inferred that the instability may be possible in the present plasma model. (basic plasma physics, plasma theory and modeling (bp))
Magnetohydrodynamic normal mode analysis of plasma with equilibrium pressure anisotropy
Fitzgerald, M; Qu, Z S
2014-01-01
In this work, we generalise linear magnetohydrodynamic (MHD) stability theory to include equilibrium pressure anisotropy in the fluid part of the analysis. A novel 'single-adiabatic' (SA) fluid closure is presented which is complementary to the usual 'double-adiabatic' (CGL) model and has the advantage of naturally reproducing exactly the MHD spectrum in the isotropic limit. As with MHD and CGL, the SA model neglects the anisotropic perturbed pressure and thus loses non-local fast-particle stabilisation present in the kinetic approach. Another interesting aspect of this new approach is that the stabilising terms appear naturally as separate viscous corrections leaving the isotropic SA closure unchanged. After verifying the self-consistency of the SA model, we re-derive the projected linear MHD set of equations required for stability analysis of tokamaks in the MISHKA code. The cylindrical wave equation is derived analytically as done previously in the spectral theory of MHD and clear predictions are made for ...
Liu, Xiaoyan; Liu, Yujuan; Zheng, Yujun
2016-02-01
In this letter, the charge transfer mobility of naphthalenediimide (NDTI) derivative is investigated. By employing the normal-mode analysis and bond length relaxation analysis, the influences of chemical elements on reorganization energies and intermolecular electronic couplings are investigated in NDTI derivative. The results show that the introduction of atom O would decrease reorganization energy in hole-hopping process and increase electronic coupling. This analysis encourages the molecular and material design in organic semiconductors.
Lu, Mingyang; Ma, Jianpeng
2011-01-01
A new method for normal mode analysis is reported for all-atom structures using molecular geometry restraints (MGR). Similar to common molecular mechanics force fields, the MGR potential contains short- and long-range terms. The short-range terms are defined by molecular geometry, i.e. bond lengths, angles and dihedrals; the long-range term is similar to that in elastic network models. Each interaction term uses a single force constant parameter, and is determined by fitting against a set of ...
Nucleosomes, which contain DNA and proteins, are the basic unit of eukaryotic chromatins. Polymers such as DNA and proteins are dynamic, and their conformational changes can lead to functional changes. Periodic dinucleotide patterns exist in nucleosomal DNA chains and play an important role in the nucleosome structure. In this paper, we use normal mode analysis to detect significant structural deformations of nucleosomal DNA and investigate the relationship between periodic dinucleotides and DNA motions. We have found that periodic dinucleotides are usually located at the peaks or valleys of DNA and protein motions, revealing that they dominate the nucleosome dynamics. Also, a specific dinucleotide pattern CA/TG appears most frequently
Analysis of vibrating structures with localized nonlinearities using nonlinear normal modes
This work is a collaboration between EDF R and D and the Laboratory of Mechanics and Acoustics. The objective is to develop theoretical and numerical tools to compute nonlinear normal modes (NNMs) of structures with localized nonlinearities. We use an approach combining the harmonic balance and the asymptotic numerical methods, known for its robustness principally for smooth systems. Regularization techniques are used to apply this approach for the study of non-smooth problems. Moreover, several aspects of the method are improved to allow the computation of NNMs for systems with a high number of degrees of freedom (DOF). Finally, the method is implemented in Code-Aster, an open-source finite element solver developed by EDF R and D. The nonlinear normal modes of a two degrees-of-freedom system are studied and some original characteristics are observed. These observations are then used to develop a methodology for the study of systems with a high number of DOFs. The developed method is finally used to compute the NNMs for a model U-tube of a nuclear plant steam generator. The analysis of the NNMs reveals the presence of an interaction between an out-of-plane (low frequency) and an in-plane (high frequency) modes, a result also confirmed by the experiment. This modal interaction is not possible using linear modal analysis and confirms the interest of NNMs as a diagnostic tool in structural dynamics. (author)
Qi Wang
Full Text Available The energy minimization of a small molecule alone does not automatically stop at a local minimum of the potential energy surface of the molecule if the minimum is shallow, thus leading to folding of the molecule and consequently hampering the generation of the bound conformation of a guest in the absence of its host. This questions the practicality of virtual screening methods that use conformations at local minima of their potential energy surfaces (local minimum conformations as potential bound conformations. Here we report a normal-mode-analysis-monitored energy minimization (NEM procedure that generates local minimum conformations as potential bound conformations. Of 22 selected guest-host complex crystal structures with guest structures possessing up to four rotatable bonds, all complexes were reproduced, with guest mass-weighted root mean square deviations of <1.0 A, through docking with the NEM-generated guest local minimum conformations. An analysis of the potential energies of these local minimum conformations showed that 22 (100%, 18 (82%, 16 (73%, and 12 (55% of the 22 guest bound conformations in the crystal structures had conformational strain energies of less than or equal to 3.8, 2.0, 0.6, and 0.0 kcal/mol, respectively. These results suggest that (1 the NEM procedure can generate small-molecule bound conformations, and (2 guests adopt low-strain-energy conformations for complexation, thus supporting the virtual screening methods that use local minimum conformations.
Accelerating All-Atom Normal Mode Analysis with Graphics Processing Unit.
Liu, Li; Liu, Xiaofeng; Gong, Jiayu; Jiang, Hualiang; Li, Honglin
2011-06-14
All-atom normal mode analysis (NMA) is an efficient way to predict the collective motions in a given macromolecule, which is essential for the understanding of protein biological function and drug design. However, the calculations are limited in time scale mainly because the required diagonalization of the Hessian matrix by Householder-QR transformation is a computationally exhausting task. In this paper, we demonstrate the parallel computing power of the graphics processing unit (GPU) in NMA by mapping Householder-QR transformation onto GPU using Compute Unified Device Architecture (CUDA). The results revealed that the GPU-accelerated all-atom NMA could reduce the runtime of diagonalization significantly and achieved over 20× speedup over CPU-based NMA. In addition, we analyzed the influence of precision on both the performance and the accuracy of GPU. Although the performance of GPU with double precision is weaker than that with single precision in theory, more accurate results and an acceptable speedup of double precision were obtained in our approach by reducing the data transfer time to a minimum. Finally, the inherent drawbacks of GPU and the corresponding solution to deal with the limitation in computational scale are also discussed in this study. PMID:26596427
Theory and Normal Mode Analysis of Change in Protein Vibrational Dynamics on Ligand Binding
Mortisugu, Kei [RIKEN, Japan; Njunda, Brigitte [Computational Molecular Biophysics, Interdisciplinary Center for Scientific Computing (IWR); Smith, Jeremy C [ORNL
2009-12-01
The change of protein vibrations on ligand binding is of functional and thermodynamic importance. Here, this process is characterized using a simple analytical 'ball-and-spring' model and all-atom normal-mode analysis (NMA) of the binding of the cancer drug, methotrexate (MTX) to its target, dihydrofolate reductase (DHFR). The analytical model predicts that the coupling between protein vibrations and ligand external motion generates entropy-rich, low-frequency vibrations in the complex. This is consistent with the atomistic NMA which reveals vibrational softening in forming the DHFR-MTX complex, a result also in qualitative agreement with neutron-scattering experiments. Energy minimization of the atomistic bound-state (B) structure while gradually decreasing the ligand interaction to zero allows the generation of a hypothetical 'intermediate' (I) state, without the ligand force field but with a structure similar to that of B. In going from I to B, it is found that the vibrational entropies of both the protein and MTX decrease while the complex structure becomes enthalpically stabilized. However, the relatively weak DHFR:MTX interaction energy results in the net entropy gain arising from coupling between the protein and MTX external motion being larger than the loss of vibrational entropy on complex formation. This, together with the I structure being more flexible than the unbound structure, results in the observed vibrational softening on ligand binding.
Normal mode analysis of macromolecular systems with the mobile block Hessian method
Until recently, normal mode analysis (NMA) was limited to small proteins, not only because the required energy minimization is a computationally exhausting task, but also because NMA requires the expensive diagonalization of a 3Na×3Na matrix with Na the number of atoms. A series of simplified models has been proposed, in particular the Rotation-Translation Blocks (RTB) method by Tama et al. for the simulation of proteins. It makes use of the concept that a peptide chain or protein can be seen as a subsequent set of rigid components, i.e. the peptide units. A peptide chain is thus divided into rigid blocks with six degrees of freedom each. Recently we developed the Mobile Block Hessian (MBH) method, which in a sense has similar features as the RTB method. The main difference is that MBH was developed to deal with partially optimized systems. The position/orientation of each block is optimized while the internal geometry is kept fixed at a plausible - but not necessarily optimized - geometry. This reduces the computational cost of the energy minimization. Applying the standard NMA on a partially optimized structure however results in spurious imaginary frequencies and unwanted coordinate dependence. The MBH avoids these unphysical effects by taking into account energy gradient corrections. Moreover the number of variables is reduced, which facilitates the diagonalization of the Hessian. In the original implementation of MBH, atoms could only be part of one rigid block. The MBH is now extended to the case where atoms can be part of two or more blocks. Two basic linkages can be realized: (1) blocks connected by one link atom, or (2) by two link atoms, where the latter is referred to as the hinge type connection. In this work we present the MBH concept and illustrate its performance with the crambin protein as an example
Twist–radial normal mode analysis in double-stranded DNA chains
We study the normal modes of a duplex DNA chain at low temperatures. We consider the coupling between the hydrogen-bond radial oscillations and the twisting motion of each base pair within the Peyrard–Bishop–Dauxois model. The coupling is mediated by the stacking interaction between adjacent base pairs along the helix. We explicitly consider different mass values for different nucleotides, extending previous works. We disclose several resonance conditions of interest, determined by the fine-tuning of certain model parameters. The role of these dynamical effects on the DNA chain charge transport properties is discussed.
Twist-radial normal mode analysis in double-stranded DNA chains
Torrellas, Germán; Maciá, Enrique
2012-10-01
We study the normal modes of a duplex DNA chain at low temperatures. We consider the coupling between the hydrogen-bond radial oscillations and the twisting motion of each base pair within the Peyrard-Bishop-Dauxois model. The coupling is mediated by the stacking interaction between adjacent base pairs along the helix. We explicitly consider different mass values for different nucleotides, extending previous works. We disclose several resonance conditions of interest, determined by the fine-tuning of certain model parameters. The role of these dynamical effects on the DNA chain charge transport properties is discussed.
Guo, Jianguang; Ward, Joshua M; Prohofsky, Earl W
2010-01-01
Self Consistent Normal Mode Analysis (SCNMA) is applied to heme c type cytochrome f to study temperature dependent protein motion. Classical Normal Mode Analysis (NMA) assumes harmonic behavior and the protein Mean Square Displacement (MSD) has a linear dependence on temperature. This is only consistent with low temperature experimental results. To connect the protein vibrational motions between low temperature and physiological temperature, we have incorporated a fitted set of anharmonic potentials into SCNMA. In addition, Quantum Harmonic Oscillator (QHO) theory has been used to calculate the displacement distribution for individual vibrational modes. We find that the modes involving soft bonds exhibit significant non-Gaussian dynamics at physiological temperature, which suggests it may be the cause of the non-Gaussian behavior of the protein motions probed by Elastic Incoherent Neutron Scattering (EINS). The combined theory displays a dynamical transition caused by the softening of few "torsional" modes in...
Matsumoto, Atsushi; Kamata, Tetsuji; Takagi, Junichi; Iwasaki, Kenji; Yura, Kei
2008-01-01
Integrin, a membrane protein with a huge extracellular domain, participates in cell-cell and cell-extracellular-matrix interactions for metazoan. A group of integrins is known to perform a large-scale structural change when the protein is activated, but the activation mechanism and generality of the conformational change remain to be elucidated. We performed normal-mode analysis of the elastic network model on integrin α V β 3 ectodomain in the bent form and identified key residues that influ...
A NEW MOMENT METHOD FOR THE FAST AND ACCURATE ANALYSIS OF NORMAL MODE HELICAL ANTENNAS
Ji Yicai; Sun Baohua; Liu Qizhong
2001-01-01
In this letter, a new moment method using helical segments is presented to model Normal Mode Helical Antenna (NMHA). Using this method, the NMHA can be modeled by a few segments. The current distributions and radiation patterns of some NMHAs are calculated.A comparison is made between results obtained using this helical segment algorithm and a linear segment algorithm, and the results of the two algorithms agree fairly well. When calculating the impedance matrix [Z], all the elements of the matrix can be obtained by only calculating a few elements with the application of the symmetric and periodic characteristics of the NMHA.Therefore, the CPU time and the memory storage are significantly reduced, with the accuracy and speed enhanced.
On the sensitivity of protein data bank normal mode analysis: an application to GH10 xylanases
Tirion, Monique M.
2015-12-01
Protein data bank entries obtain distinct, reproducible flexibility characteristics determined by normal mode analyses of their three dimensional coordinate files. We study the effectiveness and sensitivity of this technique by analyzing the results on one class of glycosidases: family 10 xylanases. A conserved tryptophan that appears to affect access to the active site can be in one of two conformations according to x-ray crystallographic electron density data. The two alternate orientations of this active site tryptophan lead to distinct flexibility spectra, with one orientation thwarting the oscillations seen in the other. The particular orientation of this sidechain furthermore affects the appearance of the motility of a distant, C terminal region we term the mallet. The mallet region is known to separate members of this family of enzymes into two classes.
Hayward, S.; Kitao, A.; Berendsen, H.J.C.
1997-01-01
Model-free methods are introduced to determine quantities pertaining to protein domain motions from normal mode analyses and molecular dynamics simulations, For the normal mode analysis, the methods are based on the assumption that in low frequency modes, domain motions can be well approximated by m
Computer simulation of ionic conduction in ZrF4-BaF2 glass: II. Normal-mode analysis
Ionic conduction in ZrF4-BaF2 glass is investigated using normal-mode analysis (NMA). The origin of two distinct timescales observed in an earlier nuclear magnetic resonance (NMR) study (Y Kawamoto and J Fujiwara 1990 Phys. Chem. Glasses 31 117) is considered. First, it is shown that the present NMA gives a result that is satisfactorily consistent with molecular dynamics (MD) simulations. This indicates that the NMA method could be successfully applied to the present topic, as well as providing added support to the MD result. The two methods give a consistent explanation for the origin of the NMR observation; the fact that there are two timescales is attributable to the difference in mobility between two classes of fluoride ions, i.e., bridging fluoride (BF) and non-bridging fluoride (NBF). The present NMA also provides information additional to that from the MD results. The difference in mobility between BF and NBF becomes significant only below the glass transition temperature Tg. Further analysis has been made to characterize the conduction mechanism more clearly, by the use of normal-mode excitations. The main finding is that an activation process becomes important for BF conduction below Tg, whereas no such process is observed for NBF. (author)
All-atom normal-mode analysis reveals an RNA-induced allostery in a bacteriophage coat protein
Dykeman, Eric C.; Twarock, Reidun
2010-03-01
Assembly of the T=3 bacteriophage MS2 is initiated by the binding of a 19 nucleotide RNA stem loop from within the phage genome to a symmetric coat protein dimer. This binding event effects a folding of the FG loop in one of the protein subunits of the dimer and results in the formation of an asymmetric dimer. Since both the symmetric and asymmetric forms of the dimer are needed for the assembly of the protein container, this allosteric switch plays an important role in the life cycle of the phage. We provide here details of an all-atom normal-mode analysis of this allosteric effect. The results suggest that asymmetric contacts between the A -duplex RNA phosphodiester backbone of the stem loop with the EF loop in one coat protein subunit results in an increased dynamic behavior of its FG loop. The four lowest-frequency modes, which encompass motions predominantly on the FG loops, account for over 90% of the increased dynamic behavior due to a localization of the vibrational pattern on a single FG loop. Finally, we show that an analysis of the allosteric effect using an elastic network model fails to predict this localization effect, highlighting the importance of using an all-atom full force field method for this problem.
Morelli, A.; Azzara, R. M.; Cavaliere, A.; Zaccarelli, L.
2014-12-01
Analysis of the oscillations of buildings — either excited by earthquakes or by ambient noise — has become an effective tool to evaluate the response of such structures to strong ground motion, and hence to assess their seismic vulnerability. Response to small-amplitude ground motion may also provide crucial information on the elastic and anelastic properties of a structure — essential in the case of historical buildings — and constrain numerical full dynamic structural analyses. We report about an analysis carried out for a tall medieval monumental building in the urban center of the Norther Italian city of Bologna. Seismic monitoring, carried on for six months using field seismic instrumentation, has revealed the response to ambient noise, and has allowed to reconstruct, with high detail, the free oscillation modes of the tower. At 97 meters, the XII-century tower of the Asinelli is the tallest masonry building in Europe, and the most slender. We measured the fundamental, and several higher-order, flexural normal modes of oscillation, as well as the fundamental torsional mode. Asymmetry due to non-coincidence of centers of mass and of stiffness produces slightly different modal frequencies of oscillation in two orthogonal directions, consistently with dynamical modeling. Horizontal particle-motion polarization plots show the cyclic energy transfer between two degrees of freedom of the system. The Asinelli spectral signature can also be easily recognized in the motion recorded at the base of nearby Garisenda. We verify that there is correlation of spectral amplitudes with time of the day — in agreement with expected time-variance of anthropic disturbance —- but also with wind velocity and, intriguingly, with temperature variations inside the buidings. We are using these data to adjust the numerical dynamical models of the buildings, to examine time variations of behavior, and to identify the origin of anthropogenic sources of vibration in view of their
Coutant, Antonin; Michel, Florent; Parentani, Renaud
2016-06-01
Black hole dynamical instabilities have been mostly studied in specific models. We here study the general properties of the complex-frequency modes responsible for such instabilities, guided by the example of a charged scalar field in an electrostatic potential. We show that these modes are square integrable, have a vanishing conserved norm, and appear in mode doublets or quartets. We also study how they appear in the spectrum and how their complex frequencies subsequently evolve when varying some external parameter. When working on an infinite domain, they appear from the reservoir of quasi-normal modes obeying outgoing boundary conditions. This is illustrated by generalizing, in a non-positive definite Krein space, a solvable model (Friedrichs model) which originally describes the appearance of a resonance when coupling an isolated system to a mode continuum. In a finite spatial domain instead, they arise from the fusion of two real frequency modes with opposite norms, through a process that closely resembles avoided crossing.
Fischer, Sean A.; Ueltschi, Tyler W.; El-Khoury, Patrick Z.; Mifflin, Amanda L.; Hess, Wayne P.; Wang, Hongfei; Cramer, Christopher J.; Govind, Niranjan
2016-03-03
Carbon-hydrogen (C-H) vibration modes serve as key probes in the chemical iden- tication of hydrocarbons and in vibrational sum-frequency generation (SFG) spec- *troscopy of hydrocarbons at the liquid/gas interface. Their assignments pose a chal- lenge from a theoretical viewpoint. In this work, we present a detailed study of the C-H stretching region of dimethyl sulfoxide (DMSO) using a new Gaussian basis set- based ab initio molecular dynamics (AIMD) module that we have implemented in the NWChem computational chemistry program. By combining AIMD simulations and static normal mode analysis, we interpret experimental infrared and Raman spectra and explore the role of anharmonic effects in this system. Our anharmonic normal mode analysis of the in-phase and out-of-phase symmetric C-H stretching modes chal- lenges the previous experimental assignment of the shoulder in the symmetric C-H stretching peak as an overtone or Fermi resonance. In addition, our AIMD simulations also show signicant broadening of the in-phase symmetric C-H stretching resonance, which suggests that the experimentally observed shoulder is due to thermal broadening of the symmetric stretching resonance.
Téllez S, Claudio A; Costa, Anilton C; Mondragón, M A; Ferreira, Glaucio B; Versiane, O; Rangel, J L; Lima, G Müller; Martin, A A
2016-12-01
Theoretical and experimental bands have been assigned for the Fourier Transform Infrared and Raman spectra of the bis(diethyldithiocarbamate)Mn(II) complex, [Mn(DDTC)2]. The calculations have been based on the DFT/B3LYP method, second derivative spectra and band deconvolution analysis. The UV-vis experimental spectra were measured in acetonitrile solution, and the calculated electronic spectrum was obtained using the TD/B3LYP method with 6-311G(d, p) basis set for all atoms. Charge transfer bands and those d-d spin forbidden were assigned in the UV-vis spectrum. The natural bond orbital analysis was carried out using the DFT/B3LYP method and the Mn(II) hybridization leading to the planar geometry of the framework was discussed. Surface enhanced Raman scattering (SERS) was also performed. Mulliken charges of the normal modes were obtained and related to the SERS enhanced bands. PMID:27344520
Guo, Y. Q.; Chen, W. Q.; Pao, Y.-H.
2008-11-01
The formulation of reverberation-ray matrix analysis has been proposed to study wave propagation in planar frames. It is applied here to modal analysis of complex three-dimensional framed structures, optionally with lumped masses and/or elastic supports. Furthermore, by means of Betti's reciprocity theorem, orthogonal conditions are established for different natural modes, and hence transient response analysis based on mode superposition is developed. Both the reverberation-ray matrix analysis for free vibration and the mode superposition method for transient response are illustrated by numerical examples.
For over a century, vibrational spectroscopy has enhanced the study of materials. Yet, assignment of particular molecular motions to vibrational excitations has relied on indirect methods. Here, we demonstrate that applying group theoretical methods to the dynamic pair distribution function analysis of neutron scattering data provides direct access to the individual atomic displacements responsible for these excitations. Applied to the molecule-based frustrated magnet with a potential magnetic valence-bond state, LiZn2Mo3O8, this approach allows direct assignment of the constrained rotational mode of Mo3O13 clusters and internal modes of MoO6 polyhedra. We anticipate that coupling this well known data analysis technique with dynamic pair distribution function analysis will have broad application in connecting structural dynamics to physical properties in a wide range of molecular and solid state systems
Fry-Petit, A M; Rebola, A F; Mourigal, M; Valentine, M; Drichko, N; Sheckelton, J P; Fennie, C J; McQueen, T M
2015-09-28
For over a century, vibrational spectroscopy has enhanced the study of materials. Yet, assignment of particular molecular motions to vibrational excitations has relied on indirect methods. Here, we demonstrate that applying group theoretical methods to the dynamic pair distribution function analysis of neutron scattering data provides direct access to the individual atomic displacements responsible for these excitations. Applied to the molecule-based frustrated magnet with a potential magnetic valence-bond state, LiZn2Mo3O8, this approach allows direct assignment of the constrained rotational mode of Mo3O13 clusters and internal modes of MoO6 polyhedra. We anticipate that coupling this well known data analysis technique with dynamic pair distribution function analysis will have broad application in connecting structural dynamics to physical properties in a wide range of molecular and solid state systems. PMID:26429001
Fry-Petit, A. M., E-mail: mcqueen@jhu.edu, E-mail: afry@fullerton.edu; Sheckelton, J. P.; McQueen, T. M., E-mail: mcqueen@jhu.edu, E-mail: afry@fullerton.edu [Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218 (United States); Institute for Quantum Matter and Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218 (United States); Department of Materials Science and Engineering, Johns Hopkins University, Baltimore, Maryland 21218 (United States); Rebola, A. F.; Fennie, C. J. [Department of Applied Physics, Cornell University, Ithaca, New York 14853 (United States); Mourigal, M.; Valentine, M.; Drichko, N. [Institute for Quantum Matter and Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218 (United States)
2015-09-28
For over a century, vibrational spectroscopy has enhanced the study of materials. Yet, assignment of particular molecular motions to vibrational excitations has relied on indirect methods. Here, we demonstrate that applying group theoretical methods to the dynamic pair distribution function analysis of neutron scattering data provides direct access to the individual atomic displacements responsible for these excitations. Applied to the molecule-based frustrated magnet with a potential magnetic valence-bond state, LiZn{sub 2}Mo{sub 3}O{sub 8}, this approach allows direct assignment of the constrained rotational mode of Mo{sub 3}O{sub 13} clusters and internal modes of MoO{sub 6} polyhedra. We anticipate that coupling this well known data analysis technique with dynamic pair distribution function analysis will have broad application in connecting structural dynamics to physical properties in a wide range of molecular and solid state systems.
Membrane proteins play critically important roles in many cellular activities such as ions and small molecule transportation, signal recognition, and transduction. In order to fulfill their functions, these proteins must be placed in different membrane environments and a variety of protein-lipid interactions may affect the behavior of these proteins. One of the key effects of protein-lipid interactions is their ability to change the dynamics status of membrane proteins, thus adjusting their functions. Here, we present a multi-scaled normal mode analysis (mNMA) method to study the dynamics perturbation to the membrane proteins imposed by lipid bi-layer membrane fluctuations. In mNMA, channel proteins are simulated at all-atom level while the membrane is described with a coarse-grained model. mNMA calculations clearly show that channel gating motion can tightly couple with a variety of membrane deformations, including bending and twisting. We then examined bi-channel systems where two channels were separated with different distances. From mNMA calculations, we observed both positive and negative gating correlations between two neighboring channels, and the correlation has a maximum as the channel center-to-center distance is close to 2.5 times of their diameter. This distance is larger than recently found maximum attraction distance between two proteins embedded in membrane which is 1.5 times of the protein size, indicating that membrane fluctuation might impose collective motions among proteins within a larger area. The hybrid resolution feature in mNMA provides atomic dynamics information for key components in the system without costing much computer resource. We expect it to be a conventional simulation tool for ordinary laboratories to study the dynamics of very complicated biological assemblies. The source code is available upon request to the authors
Wu, Xiaokun; Han, Min; Ming, Dengming, E-mail: dming@fudan.edu.cn [Department of Physiology and Biophysics, School of Life Sciences, Fudan University, Shanghai (China)
2015-10-07
Membrane proteins play critically important roles in many cellular activities such as ions and small molecule transportation, signal recognition, and transduction. In order to fulfill their functions, these proteins must be placed in different membrane environments and a variety of protein-lipid interactions may affect the behavior of these proteins. One of the key effects of protein-lipid interactions is their ability to change the dynamics status of membrane proteins, thus adjusting their functions. Here, we present a multi-scaled normal mode analysis (mNMA) method to study the dynamics perturbation to the membrane proteins imposed by lipid bi-layer membrane fluctuations. In mNMA, channel proteins are simulated at all-atom level while the membrane is described with a coarse-grained model. mNMA calculations clearly show that channel gating motion can tightly couple with a variety of membrane deformations, including bending and twisting. We then examined bi-channel systems where two channels were separated with different distances. From mNMA calculations, we observed both positive and negative gating correlations between two neighboring channels, and the correlation has a maximum as the channel center-to-center distance is close to 2.5 times of their diameter. This distance is larger than recently found maximum attraction distance between two proteins embedded in membrane which is 1.5 times of the protein size, indicating that membrane fluctuation might impose collective motions among proteins within a larger area. The hybrid resolution feature in mNMA provides atomic dynamics information for key components in the system without costing much computer resource. We expect it to be a conventional simulation tool for ordinary laboratories to study the dynamics of very complicated biological assemblies. The source code is available upon request to the authors.
Wu, Xiaokun; Han, Min; Ming, Dengming
2015-10-01
Membrane proteins play critically important roles in many cellular activities such as ions and small molecule transportation, signal recognition, and transduction. In order to fulfill their functions, these proteins must be placed in different membrane environments and a variety of protein-lipid interactions may affect the behavior of these proteins. One of the key effects of protein-lipid interactions is their ability to change the dynamics status of membrane proteins, thus adjusting their functions. Here, we present a multi-scaled normal mode analysis (mNMA) method to study the dynamics perturbation to the membrane proteins imposed by lipid bi-layer membrane fluctuations. In mNMA, channel proteins are simulated at all-atom level while the membrane is described with a coarse-grained model. mNMA calculations clearly show that channel gating motion can tightly couple with a variety of membrane deformations, including bending and twisting. We then examined bi-channel systems where two channels were separated with different distances. From mNMA calculations, we observed both positive and negative gating correlations between two neighboring channels, and the correlation has a maximum as the channel center-to-center distance is close to 2.5 times of their diameter. This distance is larger than recently found maximum attraction distance between two proteins embedded in membrane which is 1.5 times of the protein size, indicating that membrane fluctuation might impose collective motions among proteins within a larger area. The hybrid resolution feature in mNMA provides atomic dynamics information for key components in the system without costing much computer resource. We expect it to be a conventional simulation tool for ordinary laboratories to study the dynamics of very complicated biological assemblies. The source code is available upon request to the authors.
Analog gravity from field theory normal modes?
Barcelo, C; Visser, M; Barcelo, Carlos; Liberati, Stefano; Visser, Matt
2001-01-01
We demonstrate that the emergence of a curved spacetime ``effective Lorentzian geometry'' is a common and generic result of linearizing a field theory around some non-trivial background. This investigation is motivated by considering the large number of ``analog models'' of general relativity that have recently been developed based on condensed matter physics, and asking whether there is something more fundamental going on. Indeed, linearization of a classical field theory (a field theoretic ``normal mode analysis'') results in fluctuations whose propagation is governed by a Lorentzian-signature curved spacetime ``effective metric''. For a single scalar field, this procedure results in a unique effective metric, which is quite sufficient for simulating kinematic aspects of general relativity (up to and including Hawking radiation). Quantizing the linearized fluctuations, the one-loop effective action contains a term proportional to the Einstein--Hilbert action, suggesting that while classical physics is respo...
The effective degeneracy of protein normal modes
Na, Hyuntae; Song, Guang
2016-06-01
Normal modes are frequently computed and used to portray protein dynamics and interpret protein conformational changes. In this work, we investigate the nature of normal modes and find that the normal modes of proteins, especially those at the low frequency range (0–600 cm‑1), are highly susceptible to degeneracy. Two or more modes are degenerate if they have the same frequency and consequently any orthogonal transformation of them also is a valid representation of the mode subspace. Thus, degenerate modes can no longer characterize unique directions of motions as regular modes do. Though the normal modes of proteins are usually of different frequencies, the difference in frequency between neighboring modes is so small that, under even slight structural uncertainty that unavoidably exists in structure determination, it can easily vanish and as a result, a mode becomes effectively degenerate with its neighboring modes. This can be easily observed in that some modes seem to disappear and their matching modes cannot be found when the structure used to compute the modes is modified only slightly. We term this degeneracy the effective degeneracy of normal modes. This work is built upon our recent discovery that the vibrational spectrum of globular proteins is universal. The high density of modes observed in the vibrational frequency spectra of proteins renders their normal modes highly susceptible to degeneracy, under even the smallest structural uncertainty. Indeed, we find the degree of degeneracy of modes is proportional to the density of modes in the vibrational spectrum. This means that for modes at the same frequency, degeneracy is more severe for larger proteins. Degeneracy exists also in the modes of coarse-grained models, but to a much lesser extent than those of all-atom models. In closing, we discuss the implications of the effective degeneracy of normal modes: how it may significantly affect the ways in which normal modes are used in various normal modes
WEBnm@: a web application for normal mode analyses of proteins
Reuter Nathalie
2005-03-01
Full Text Available Abstract Background Normal mode analysis (NMA has become the method of choice to investigate the slowest motions in macromolecular systems. NMA is especially useful for large biomolecular assemblies, such as transmembrane channels or virus capsids. NMA relies on the hypothesis that the vibrational normal modes having the lowest frequencies (also named soft modes describe the largest movements in a protein and are the ones that are functionally relevant. Results We developed a web-based server to perform normal modes calculations and different types of analyses. Starting from a structure file provided by the user in the PDB format, the server calculates the normal modes and subsequently offers the user a series of automated calculations; normalized squared atomic displacements, vector field representation and animation of the first six vibrational modes. Each analysis is performed independently from the others and results can be visualized using only a web browser. No additional plug-in or software is required. For users who would like to analyze the results with their favorite software, raw results can also be downloaded. The application is available on http://www.bioinfo.no/tools/normalmodes. We present here the underlying theory, the application architecture and an illustration of its features using a large transmembrane protein as an example. Conclusion We built an efficient and modular web application for normal mode analysis of proteins. Non specialists can easily and rapidly evaluate the degree of flexibility of multi-domain protein assemblies and characterize the large amplitude movements of their domains.
Neutrino induced vorticity, Alfven waves and the normal modes
Bhatt, Jitesh R
2016-01-01
We consider plasma consisting of electrons and ions in presence of a background neutrino gas and develop the magneto hydrodynamic equations for the system. We show that electron neutrino interaction can induce vorticity in the plasma even in the absence of any electromagnetic perturbations if the background neutrino density is left-right asymmetric. This induced vorticity support a new kind of mode which will vanish when the background neutrino asymmetry vanishes. The normal mode analysis of the equations is done to show that, in the presence of neutrino back-ground, the normal modes get modified and the corrections are proportional to the neutrino asymmetry parameter.
Instantaneous Normal Modes and the Protein Glass Transition
Schultz, Roland [University of Tennessee, Knoxville (UTK); Krishnan, Marimuthu [ORNL; Daidone, Isabella [University of Heidelberg; Smith, Jeremy C [ORNL
2009-01-01
In the instantaneous normal mode method, normal mode analysis is performed at instantaneous configurations of a condensed-phase system, leading to modes with negative eigenvalues. These negative modes provide a means of characterizing local anharmonicities of the potential energy surface. Here, we apply instantaneous normal mode to analyze temperature-dependent diffusive dynamics in molecular dynamics simulations of a small protein (a scorpion toxin). Those characteristics of the negative modes are determined that correlate with the dynamical (or glass) transition behavior of the protein, as manifested as an increase in the gradient with T of the average atomic mean-square displacement at 220 K. The number of negative eigenvalues shows no transition with temperature. Further, although filtering the negative modes to retain only those with eigenvectors corresponding to double-well potentials does reveal a transition in the hydration water, again, no transition in the protein is seen. However, additional filtering of the protein double-well modes, so as to retain only those that, on energy minimization, escape to different regions of configurational space, finally leads to clear protein dynamical transition behavior. Partial minimization of instantaneous configurations is also found to remove nondiffusive imaginary modes. In summary, examination of the form of negative instantaneous normal modes is shown to furnish a physical picture of local diffusive dynamics accompanying the protein glass transition.
Instantaneous Normal Modes and the Protein Glass Transition
In the instantaneous normal mode method, normal mode analysis is performed at instantaneous configurations of a condensed-phase system, leading to modes with negative eigenvalues. These negative modes provide a means of characterizing local anharmonicities of the potential energy surface. Here, we apply instantaneous normal mode to analyze temperature-dependent diffusive dynamics in molecular dynamics simulations of a small protein (a scorpion toxin). Those characteristics of the negative modes are determined that correlate with the dynamical (or glass) transition behavior of the protein, as manifested as an increase in the gradient with T of the average atomic mean-square displacement at 220 K. The number of negative eigenvalues shows no transition with temperature. Further, although filtering the negative modes to retain only those with eigenvectors corresponding to double-well potentials does reveal a transition in the hydration water, again, no transition in the protein is seen. However, additional filtering of the protein double-well modes, so as to retain only those that, on energy minimization, escape to different regions of configurational space, finally leads to clear protein dynamical transition behavior. Partial minimization of instantaneous configurations is also found to remove nondiffusive imaginary modes. In summary, examination of the form of negative instantaneous normal modes is shown to furnish a physical picture of local diffusive dynamics accompanying the protein glass transition
Palys, Barbara J.; Ham, van den Dirk M.W.; Briels, Wim; Feil, Dirk
1995-01-01
Resonance Raman spectra of monolayers of transition metal phthalocyanines reveal specific interaction with the support. To elucidate its mechanism, Raman spectra of zinc phthalocyanine monolayers were studied. The analysis was based largely on the results of MNDO calculations. Calculated wavenumbers
A spectral characterization of nonlinear normal modes
Cirillo, G. I.; Mauroy, A.; Renson, L.; Kerschen, G.; Sepulchre, R.
2016-09-01
This paper explores the relationship that exists between nonlinear normal modes (NNMs) defined as invariant manifolds in phase space and the spectral expansion of the Koopman operator. Specifically, we demonstrate that NNMs correspond to zero level sets of specific eigenfunctions of the Koopman operator. Thanks to this direct connection, a new, global parametrization of the invariant manifolds is established. Unlike the classical parametrization using a pair of state-space variables, this parametrization remains valid whenever the invariant manifold undergoes folding, which extends the computation of NNMs to regimes of greater energy. The proposed ideas are illustrated using a two-degree-of-freedom system with cubic nonlinearity.
Normal Modes of Black Hole Accretion Disks
Ortega-Rodriguez, Manuel; /Stanford U., Appl. Phys. Dept. /Costa Rica U.; Silbergleit, Alexander S.; /Stanford U., HEPL; Wagoner, Robert V.; /Stanford U., Phys. Dept.
2006-11-07
This paper studies the hydrodynamical problem of normal modes of small adiabatic oscillations of relativistic barotropic thin accretion disks around black holes (and compact weakly magnetic neutron stars). Employing WKB techniques, we obtain the eigen frequencies and eigenfunctions of the modes for different values of the mass and angular momentum of the central black hole. We discuss the properties of the various types of modes and examine the role of viscosity, as it appears to render some of the modes unstable to rapid growth.
Comparative Investigation of Normal Modes and Molecular Dynamics of Hepatitis C NS5B Protein
Asafi, M. S.; Yildirim, A.; Tekpinar, M.
2016-04-01
Understanding dynamics of proteins has many practical implications in terms of finding a cure for many protein related diseases. Normal mode analysis and molecular dynamics methods are widely used physics-based computational methods for investigating dynamics of proteins. In this work, we studied dynamics of Hepatitis C NS5B protein with molecular dynamics and normal mode analysis. Principal components obtained from a 100 nanoseconds molecular dynamics simulation show good overlaps with normal modes calculated with a coarse-grained elastic network model. Coarse-grained normal mode analysis takes at least an order of magnitude shorter time. Encouraged by this good overlaps and short computation times, we analyzed further low frequency normal modes of Hepatitis C NS5B. Motion directions and average spatial fluctuations have been analyzed in detail. Finally, biological implications of these motions in drug design efforts against Hepatitis C infections have been elaborated.
Normal modes of confined cold ionic systems
Schiffer, J.P.; Dubin, D.H. [Univ. of California, San Diego, CA (United States)
1995-08-01
The normal modes of a cloud of confined ions forming a strongly-correlated plasma were investigated. The results of molecular-dynamics simulations were compared to predictions of a cold fluid mode. Mode frequencies are observed to shift slightly compared to the cold fluid predictions, and the modes are also observed to damp in time. Simulations also reveal a set of torsional oscillations which have no counterpart in cold fluid theory. The frequency shift, damping, and torsional effects are compared to a model that treats trapped plasmas as a visco-elastic spheroid. It may be possible to measure high-frequency bulk and shear moduli of a strongly-correlated plasma from mode excitation experiments on trapped non-neutral plasmas. An example of the results of the calculation is presented.
Response and normal modes of a system in the electric and magnetic-dipole approximation
The effect of making the interaction fields evolve from a finite time of a system of molecules is studied in the electric- and magnetic-dipole approximation. Features due to the breaking up of the infinite evolution time are discussed. The resulting equations are analyzed for the response of the system. The analysis of the equations for the propagation of normal modes is manifested. The conditions under which normal modes propagate are stated. (author)
On normal modes of gas sheets and discs
A method is described for calculating the reflection and transmission coefficients characterizing normal modes of the Goldreich-Lynden-Bell gas sheet. Two families of gas discs without self-gravity for which the normal modes can be found analytically are given and used to illustrate the validity of the sheet approximation. (author)
High-Frequency Normal Mode Propagation in Aluminum Cylinders
Lee, Myung W.; Waite, William F.
2009-01-01
Acoustic measurements made using compressional-wave (P-wave) and shear-wave (S-wave) transducers in aluminum cylinders reveal waveform features with high amplitudes and with velocities that depend on the feature's dominant frequency. In a given waveform, high-frequency features generally arrive earlier than low-frequency features, typical for normal mode propagation. To analyze these waveforms, the elastic equation is solved in a cylindrical coordinate system for the high-frequency case in which the acoustic wavelength is small compared to the cylinder geometry, and the surrounding medium is air. Dispersive P- and S-wave normal mode propagations are predicted to exist, but owing to complex interference patterns inside a cylinder, the phase and group velocities are not smooth functions of frequency. To assess the normal mode group velocities and relative amplitudes, approximate dispersion relations are derived using Bessel functions. The utility of the normal mode theory and approximations from a theoretical and experimental standpoint are demonstrated by showing how the sequence of P- and S-wave normal mode arrivals can vary between samples of different size, and how fundamental normal modes can be mistaken for the faster, but significantly smaller amplitude, P- and S-body waves from which P- and S-wave speeds are calculated.
Modeling Ringdown: Beyond the Fundamental Quasi-Normal Modes
London, Lionel; Shoemaker, Deirdre
2014-01-01
While black hole perturbation theory predicts a rich quasi-normal mode structure, technical challenges have limited the numerical study of excitations to the fundamental, lowest order modes caused by the coalescence of black holes. Here, we present a robust method to identify quasi-normal mode excitations beyond the fundamentals within currently available numerical relativity waveforms. In applying this method to waveforms of initially non-spinning black hole binaries, of mass ratios 1 to 15, we find not only the fundamental quasi-normal mode amplitudes, but also overtones, and evidence for 2nd order quasi-normal modes. We find that the mass-ratio dependence of quasi-normal mode excitation is very well modeled by a Post-Newtonian like sum in symmetric mass ratio. Concurrently, we find that the mass ratio dependence of some quasi-normal modes is qualitatively different from their Post-Newtonian inspired counterparts, suggesting that the imprints of nonlinear merger are more evident in some modes than in others...
Optimization of hardening/softening behavior of plane frame structures using nonlinear normal modes
Dou, Suguang; Jensen, Jakob Søndergaard
2016-01-01
Devices that exploit essential nonlinear behavior such as hardening/softening and inter-modal coupling effects are increasingly used in engineering and fundamental studies. Based on nonlinear normal modes, we present a gradient-based structural optimization method for tailoring the hardening....../softening behavior of nonlinear mechanical systems. The iterative optimization procedure consists of calculation of nonlinear normal modes, solving an adjoint equation system for sensitivity analysis and an update of design variables using a mathematical programming tool. We demonstrate the method with examples...
"Good Vibrations": A workshop on oscillations and normal modes
Barbieri, Sara; Carpineti, Marina; Giliberti, Marco; Rigon, Enrico; Stellato, Marco; Tamborini, Marina
2016-05-01
We describe some theatrical strategies adopted in a two hour workshop in order to show some meaningful experiments and the underlying useful ideas to describe a secondary school path on oscillations, that develops from harmonic motion to normal modes of oscillations, and makes extensive use of video analysis, data logging, slow motions and applet simulations. Theatre is an extremely useful tool to stimulate motivation starting from positive emotions. That is the reason why the theatrical approach to the presentation of physical themes has been explored by the group "Lo spettacolo della Fisica" (http://spettacolo.fisica.unimi.it) of the Physics Department of University of Milano for the last ten years (Carpineti et al., JCOM, 10 (2011) 1; Nuovo Cimento B, 121 (2006) 901) and has been inserted also in the European FP7 Project TEMI (Teaching Enquiry with Mysteries Incorporated, see http://teachingmysteries.eu/en) which involves 13 different partners coming from 11 European countries, among which the Italian (Milan) group. According to the TEMI guidelines, this workshop has a written script based on emotionally engaging activities of presenting mysteries to be solved while participants have been involved in nice experiments following the developed path.
Quasi-Normal Modes of Stars and Black Holes
Kokkotas Kostas
1999-01-01
Full Text Available Perturbations of stars and black holes have been one of the main topics of relativistic astrophysics for the last few decades. They are of particular importance today, because of their relevance to gravitational wave astronomy. In this review we present the theory of quasi-normal modes of compact objects from both the mathematical and astrophysical points of view. The discussion includes perturbations of black holes (Schwarzschild, Reissner-Nordström, Kerr and Kerr-Newman and relativistic stars (non-rotating and slowly-rotating. The properties of the various families of quasi-normal modes are described, and numerical techniques for calculating quasi-normal modes reviewed. The successes, as well as the limits, of perturbation theory are presented, and its role in the emerging era of numerical relativity and supercomputers is discussed.
Normal modes of prion proteins: from native to infectious particle.
Samson, Abraham O; Levitt, Michael
2011-03-29
Prion proteins (PrP) are the infectious agent in transmissible spongiform encephalopathies (i.e., mad cow disease). To be infectious, prion proteins must undergo a conformational change involving a decrease in α-helical content along with an increase in β-strand content. This conformational change was evaluated by means of elastic normal modes. Elastic normal modes show a diminution of two α-helices by one and two residues, as well as an extension of two β-strands by three residues each, which could instigate the conformational change. The conformational change occurs in a region that is compatible with immunological studies, and it is observed more frequently in mutant prions that are prone to conversion than in wild-type prions because of differences in their starting structures, which are amplified through normal modes. These findings are valuable for our comprehension of the conversion mechanism associated with the conformational change in prion proteins. PMID:21338080
On Normal Modes of Vibrating 1-D Mechanical Systems with Discontinuous Properties
Fedorchenko, Alexander I.; Stachiv, Ivo; Wang, A. B.
2012-01-01
Roč. 19, č. 4 (2012), s. 265-270. ISSN 1537-6494 Institutional research plan: CEZ:AV0Z20760514 Keywords : dimensionless analysis * fundamental solution * normal modes Subject RIV: BI - Acoustics Impact factor: 0.701, year: 2012 http://www.tandfonline.com/doi/abs/10.1080/15376494.2011.642936
Normal Modes of Prion Proteins: From Native to Infectious particle◊
Samson, Abraham O.; Levitt, Michael
2011-01-01
Prion proteins (PrP) are the infectious agent in transmissible spongiform encephalopathies (i.e. mad cow disease). To be infectious, prion proteins must undergo a conformational change involving a decrease of α-helical content along with an increase of β-strand structure. This conformational change was evaluated by means of elastic normal modes. Elastic normal modes show a diminution of two α-helices by one and two residues, as well as an extension of two β-strands by three residues each whic...
Mean flow generation mechanism by inertial waves and normal modes
Will, Andreas; Ghasemi, Abouzar
2016-04-01
The mean flow generation mechanism by nonlinearity of the inertial normal modes and inertial wave beams in a rotating annular cavity with longitudinally librating walls in stable regime is discussed. Inertial normal modes (standing waves) are excited when libration frequency matches eigenfrequencies of the system. Inertial wave beams are produced by Ekman pumping and suction in a rotating cylinder and form periodic orbits or periodic ray trajectories at selected frequencies. Inertial wave beams emerge as concentrated shear layers in a librating annular cavity, while normal modes appear as global recirculation cells. Both (inertial wave beam and mode) are helical and thus intrinsically non-linear flow structures. No second mode or wave is necessary for non-linearity. We considered the low order normal modes (1,1), (2,1) and (2,2) which are expected to be excited in the planetary objects and investigate the mean flow generation mechanism using two independent solutions: 1) analytical solution (Borcia 2012) and 2) the wave component of the flow (ω0 component) obtained from the direct numerical simulation (DNS). It is well known that a retrograde bulk mean flow is generated by the Ekman boundary layer and E1/4-Stewartson layer close to the outer cylinder side wall due to libration. At and around the normal mode resonant frequencies we found additionally a prograde azimuthal mean flow (Inertial Normal Mode Mean Flow: INMMF) in the bulk of the fluid. The fluid in the bulk is in geostrophic balance in the absence of the inertial normal modes. However, when INMMF is excited, we found that the geostrophic balance does not hold in the region occupied by INMMF. We hypothesize that INMMF is generated by the nonlinearity of the normal modes or by second order effects. Expanding the velocity {V}(u_r,u_θ,u_z) and pressure (p) in a power series in ɛ (libration amplitude), the Navier-Stokes equations are segregated into the linear and nonlinear parts at orders ɛ1 and ɛ^2
Numerical computation of nonlinear normal modes in mechanical engineering
Renson, L.; Kerschen, G.; Cochelin, B.
2016-03-01
This paper reviews the recent advances in computational methods for nonlinear normal modes (NNMs). Different algorithms for the computation of undamped and damped NNMs are presented, and their respective advantages and limitations are discussed. The methods are illustrated using various applications ranging from low-dimensional weakly nonlinear systems to strongly nonlinear industrial structures.
S-Wave Normal Mode Propagation in Aluminum Cylinders
Lee, Myung W.; Waite, William F.
2010-01-01
Large amplitude waveform features have been identified in pulse-transmission shear-wave measurements through cylinders that are long relative to the acoustic wavelength. The arrival times and amplitudes of these features do not follow the predicted behavior of well-known bar waves, but instead they appear to propagate with group velocities that increase as the waveform feature's dominant frequency increases. To identify these anomalous features, the wave equation is solved in a cylindrical coordinate system using an infinitely long cylinder with a free surface boundary condition. The solution indicates that large amplitude normal-mode propagations exist. Using the high-frequency approximation of the Bessel function, an approximate dispersion relation is derived. The predicted amplitude and group velocities using the approximate dispersion relation qualitatively agree with measured values at high frequencies, but the exact dispersion relation should be used to analyze normal modes for full ranges of frequency of interest, particularly at lower frequencies.
Electromagnetic normal modes and Casimir effects in layered structures
Sernelius, Bo E
2014-01-01
We derive a general procedure for finding the electromagnetic normal modes in layered structures. We apply this procedure to planar, spherical and cylindrical structures. These normal modes are important in a variety of applications. They are the only input needed in calculations of Casimir interactions. We present explicit expression for the condition for modes and Casimir energy for a large number of specific geometries. The layers are allowed to be two-dimensional so graphene and graphene-like sheets as well as two-dimensional electron gases can be handled within the formalism. Also forces on atoms in layered structures are obtained. One side-result is the van der Waals and Casimir-Polder interaction between two atoms.
Non-linear normal modes in dynamics - discrete systems
Náprstek, Jiří; Fischer, Cyril
Vol. 821. Zürich: Trans Tech Publications, 2016 - (Fischer, C.), s. 254-265 ISBN 978-3-03835-700-1. [Engineering mechanics 2015 /21./. Svratka (CZ), 11.05.2015-14.05.2015] R&D Projects: GA ČR(CZ) GA15-01035S Institutional support: RVO:68378297 Keywords : non-linear dynamical systems * non-linear normal modes * discretization * multi-scale method Subject RIV: JM - Building Engineering
A High Resolution Normal Mode Solution of Japan Sea
Wu, Y.; Satake, K.
2014-12-01
Normal mode calculation of a semi-closed or completely closed bay or ocean basin helps us to understand the oscillation characteristics including those excited by incoming tsunamis. In addition, tsunami propagation can be synthesized by superposition of normal modes. Japan Sea is an almost closed ocean basin where many large tsunamigenic earthquakes occurred (fig. 1). Satake and Shimazaki (1988) calculated the normal modes using a 20km grid (~10' or about 2,000 ocean grids), compared the observed and calculated normal modes from the 1964 Niigata and 1983 Japan Sea earthquakes, and discussed the their different excitation characteristics . Because of development of computer and numerical computation techniques, it is worthwhile to revisit this problem. Starting from Laplace's tidal equations and ignoring the rotation of the earth, Loomis (1975) discretized the problem into the eigenvalue problem of a symmetric sparse matrix, which was solved by Householder transformations. This method is used by Satake and Shimazaki (1988) for Japan Sea and Aida (1996) for Tokyo Bay. However, this method needs O(n^3) operation in time and O(n^2) in memory (n is the total number of water grid. e.g., for Japan Sea in 30 sec grid, n~10^6), which would require a super computer.To overcome this disadvantage, we first introduce a recent iteration method called Implicitly Restarted Arnoldi Method (Lehoucq et al., 1997), which itself speeds up the calculation a bit. Then after we develop a sparse version of matrix storage and multiplication, the operation count in time and memory reduced dramatically to O(n^1.5) (including about 0.5 for iteration process) and O(n) respectively, utilizing the special property of the matrix and the iteration method. This means any current computer can easily solve a large eigenvalue problem. Earthquakes.png
Rapid simulation of protein motion: merging flexibility, rigidity and normal mode analyses
Protein function frequently involves conformational changes with large amplitude on timescales which are difficult and computationally expensive to access using molecular dynamics. In this paper, we report on the combination of three computationally inexpensive simulation methods—normal mode analysis using the elastic network model, rigidity analysis using the pebble game algorithm, and geometric simulation of protein motion—to explore conformational change along normal mode eigenvectors. Using a combination of ElNemo and First/Froda software, large-amplitude motions in proteins with hundreds or thousands of residues can be rapidly explored within minutes using desktop computing resources. We apply the method to a representative set of six proteins covering a range of sizes and structural characteristics and show that the method identifies specific types of motion in each case and determines their amplitude limits
Nonlinear normal modes in mechanical systems: concept and computation with numerical continuation
Silva Bernárdez, Alejandro
2016-01-01
The purpose of this Project is, first and foremost, to disclose the topic of nonlinear vibrations and oscillations in mechanical systems and, namely, nonlinear normal modes NNMs to a greater audience of researchers and technicians. To do so, first of all, the dynamical behavior and properties of nonlinear mechanical systems is outlined from the analysis of a pair of exemplary models with the harmonic balanced method. The conclusions drawn are contrasted with the Linear Vibration Theory. Th...
Normal Modes of the B=4 Skyrme Soliton
Barnes, C; Turok, N G; Barnes, Chris; Baskerville, Kim; Turok, Neil
1997-01-01
The Skyrme model of nuclear physics requires quantisation if it is to match observed nuclear properties. A simple technique is used to find the normal mode spectrum of the baryon number $B=4$ Skyrme soliton, representing the $\\alpha$ particle. We find sixteen vibrational modes and classify them under the cubic symmetry group $O_h$ of the static solution. The spectrum possesses a remarkable structure, with the lowest energy modes lying in those representations expected from an approximate correspondence between Skyrmions and BPS monopoles. The next mode up is the `breather', and above that are higher multipole breathing modes.
Non-linear normal modes in dynamics - discrete systems
Náprstek, Jiří; Fischer, Cyril
Prague : Institute of theoretical and applied mechanics, Academy of Sciences of the Czech Republic, v. v. i., 2015 - (Náprstek, J.; Fischer, C.). s. 208-209 ISBN 978-80-86246-42-0. ISSN 1805-8248. [ Engineering mechanics 2015 /21./. 11.05.2015-14.05.2015, Svratka] R&D Projects: GA ČR(CZ) GA15-01035S Institutional support: RVO:68378297 Keywords : nonlinear dynamic systems * non-linear normal modes * discretization * multi-scale method Subject RIV: JM - Building Engineering
Linear Plasma Oscillation Described by Superposition of Normal Modes
Pécseli, Hans
1974-01-01
The existence of steady‐state solutions to the linearized ion and electron Vlasov equation is demonstrated for longitudinal waves in an initially stable plasma. The evolution of an arbitrary initial perturbation can be described by superposition of these solutions. Some common approximations to the...... full set of equations can be solved in the same way. In some special cases, relevant, for instance, for single‐ended Q machine experiments, a problem with given boundary conditions can be solved by superposition of normal modes....
Quasi-normal modes: a simple derivation of the level spacing of the frequencies
It is known that the imaginary parts of the frequencies of the quasi-normal modes of the Schwarzschild black hole are equally spaced, with the level spacing dependent only on the surface gravity. We generalize this result to a wider class of spacetimes and provide a simple derivation of the imaginary parts of the frequencies. The analysis shows that the result is closely linked to the thermal nature of horizons and arises from the exponential redshift of the wave modes close to the horizon. (letter to the editor)
Theoretical and experimental study of the normal modes in a coupled two-dimensional system
Giménez, Marcos H; Gómez-Tejedor, José Antonio; Velazquez, Luisberis; Monsoriu, Juan A
2016-01-01
In this work, the normal modes of a two-dimensional oscillating system have been studied from a theoretical and experimental point of view. The normal frequencies predicted by the Hessian matrix for a coupled two-dimensional particle system are compared to those obtained for a real system consisting of two oscillating smartphones coupled one to the other by springs. Experiments are performed on an air table in order to remove the friction forces. The oscillation data are captured by the acceleration sensor of the smartphones and exported to file for further analysis. The experimental frequencies compare reasonably well with the theoretical predictions, namely, within 1.7 % of discrepancy.
The Temperature Dependence of Some Normal Modes in Strontium Titanate
The frequency/wave vector dispetsior curves have been measured for some of the normal modes in strontium titanate along [100]. The experiments were performed using the triple axis spectrometer at Chalk River, usually with the constant Q-bar technique. Of particular interest is the temperature dependence of the lowest transverse optical branch, which has been studied at two temperatures. The frequencies (units 1012 cycles/s) at q-bar = 0 are 1.27 ± 0.05 at 90oK and 2.73 ± 0.05 at 296oK. The dispersion curves have maximum frequencies (4.2 at 90oK, 4.4 at 296oK) near the middle of the zone; at the zone boundary the frequencies are about 3.5. The anomalous temperature dependence of the q-bar = 0 mode has been predicted by Cochran, and the magnitude of the change with temperature, which may be obtained from the temperature dependence of the dielectric constant, is in good agreement with the theory. The non-infrared active mode has been observed and has a frequency at q-bar = 0 of 7.95 ± 0.15. (author)
Quasi-Normal Modes for Subtracted Rotating and Magnetised Geometries
Cvetic, M; Saleem, Z H
2014-01-01
We obtain explicit separable solutions of the wave equation of massless minimally coupled scalar fields in the subtracted geometry of four-dimensional rotating and Melvin (magnetised) four-charge black holes of the STU model, a consistent truncation of maximally supersymmetric supergravity with four types of electromagnetic fields. These backgrounds possess a hidden SL(2,R) x SL(2,R) x SO(3) symmetry and faithfully model the near horizon geometry of these black holes, but locate them in a confining asymptotically conical box. For each subtracted geometry we obtain two branches of quasi-normal modes, given in terms of hypergeometric functions and spherical harmonics. One branch is over-damped and the other under-damped and they exhibit rotational splitting. No black hole bomb is possible because the Killing field which co-rotates with the horizon is everywhere timelike outside the black hole. A five-dimensional lift of these geometries is given locally by the product of a BTZ black hole with a a two-sphere. Th...
Friedson, Andrew James; Ding, Leon
2015-11-01
We have developed a numerical model to calculate the frequencies and eigenfunctions of adiabatic, non-radial normal-mode oscillations in the gas giants and Titan. The model solves the linearized momentum, energy, and continuity equations for the perturbation displacement, pressure, and density fields and solves Poisson’s equation for the perturbation gravitational potential. The response to effects associated with planetary rotation, including the Coriolis force, centrifugal force, and deformation of the equilibrium structure, is calculated numerically. This provides the capability to accurately compute the influence of rotation on the modes, even in the limit where mode frequency approaches the rotation rate, when analytical estimates based on functional perturbation analysis become inaccurate. This aspect of the model makes it ideal for studying the potential role of low-frequency modes for driving spiral density waves in the C ring that possess relatively low pattern speeds (Hedman, M.M and P.D. Nicholson, MNRAS 444, 1369-1388). In addition, the model can be used to explore the effect of internal differential rotation on the eigenfrequencies. We will (1) present examples of applying the model to calculate the properties of normal modes in Saturn and their relationship to observed spiral density waves in the C ring, and (2) discuss how the model is used to examine the response of the superrotating atmosphere of Titan to the gravitational tide exerted by Saturn. This research was supported by a grant from the NASA Planetary Atmosphere Program.
A Bloch mode expansion approach for analyzing quasi-normal modes in open nanophotonic structures
de Lasson, Jakob Rosenkrantz; Kristensen, Philip Trøst; Mørk, Jesper;
2014-01-01
conventional techniques. The quasi-normal modes are determined by constructing a cavity roundtrip matrix and iterating the complex mode wavelength towards a unity eigenvalue. We demonstrate the method by deter- mining quasi-normal modes of cavities in two-dimensional photonic crystals side-coupled to W1......We present a new method for determining quasi-normal modes in open nanophotonic structures using a modal ex- pansion technique. The outgoing wave boundary condition of the quasi-normal modes is satisfied automatically without absorbing boundaries, representing a significant advantage compared to...
A New Non-linear Technique for Measurement of Splitting Functions of Normal Modes of the Earth
Pachhai, S.; Masters, G.; Tkalcic, H.
2014-12-01
Normal modes are the vibrating patterns of the Earth in response to the large earthquakes. Normal mode spectra are split due to Earth's rotation, ellipticity, and heterogeneity. The normal mode splitting is visualized through splitting functions, which represent the local radial average of Earth's structure seen by a mode of vibration. The analysis of the splitting of normal modes can provide unique information about the lateral variation of the Earth's elastic properties that cannot be directly imaged in body wave tomographic images. The non-linear iterative spectral fitting of the observed complex spectra and autoregressive linear inversion have been widely utilized to compute the Earth's 3-D structure. However, the non-linear inversion requires a model of the earthquake source and the retrieved 3-D structure is sensitive to the initial constraints. In contrast, the autoregressive linear inversion does not require the source model. However, this method requires many events to achieve full convergence. In addition, significant disagreement exists between different studies because of the non-uniqueness of the problem and limitations of different methods. We thus apply the neighbourhood algorithm (NA) to measure splitting functions. The NA is an efficient model space search technique and works in two steps: In the first step, the algorithm finds all the models compatible with given data while the posterior probability density of the model parameters are obtained in the second step. The NA can address the problem of non-uniqueness by taking advantage of random sampling of the full model space. The parameter trade-offs are conveniently visualized using joint marginal distributions. In addition, structure coefficients uncertainties can be extracted from the posterior probability distribution. After demonstrating the feasibility of NA with synthetic examples, we compute the splitting functions for the mode 13S2 (sensitive to the inner core) from several large
Normal modes and quality factors of spherical dielectric resonators: I — Shielded dielectric sphere
R A Yadav; I D Singh
2004-06-01
Electromagnetic theoretic analysis of shielded homogeneous and isotropic dielectric spheres has been made. Characteristic equations for the TE and TM modes have been derived. Dielectric spheres of radii of the order of $$m size are found suitable for the optical frequency region whereas for the microwave region radii of the order of mm size are found suitable. Parameters suitable for their application in the optical and microwave frequency ranges have been used to compute the frequencies corresponding to the normal modes for the TE and TM modes. Expressions for the quality factors for realistic resonators, i.e., for a dielectric sphere with a non-zero conductivity and a metal shield with a finite conductivity have also been derived for the TE and TM modes. Computations of the quality factors have been made for resonators with parameters suitable for the optical and the microwave regions.
SwarmDock and the Use of Normal Modes in Protein-Protein Docking
Paul A. Bates
2010-09-01
Full Text Available Here is presented an investigation of the use of normal modes in protein-protein docking, both in theory and in practice. Upper limits of the ability of normal modes to capture the unbound to bound conformational change are calculated on a large test set, with particular focus on the binding interface, the subset of residues from which the binding energy is calculated. Further, the SwarmDock algorithm is presented, to demonstrate that the modelling of conformational change as a linear combination of normal modes is an effective method of modelling flexibility in protein-protein docking.
Quasi-normal Modes of Extremal Black Holes from Hidden Conformal Symmetry
Chen, Bin
2010-01-01
In this paper, we construct the quasi-normal modes of three-dimensional extremal black holes in an algebraic way. We show that the infinite towers of the quasi-normal modes of scalar, vector and tensor could be constructed as the descendents of the highest weight modes. Our investigation shows that the hidden conformal symmetry suggested in arXiv:1007.4269 is an intrinsic property of the extremal black hole. Moreover, we notice that we need to fix the freedom in defining the local vector fields and find the right hidden conformal symmetry to obtain the physical quasi-normal modes.
A comparative study of the normal modes of various modern bells
Perrin, R.; Charnley, T.
1987-09-01
Finite element calculations of the normal modes of church, carillon, hand and fire-alarm bells have been made. Some of the results are presented and comparisons made which shed new light on mode classification.
Streaky signal in seismic normal mode band observed at Syowa Station, Antarctica
早河, 秀章; 澁谷, 和雄; 土井, 浩一郎; 青山, 雄一; 金尾, 政紀; 池田, 博
2010-01-01
Background free oscillations are known as continuous and global signals on noise level in seismic normal mode band. These were found from record of superconducting gravimeter (SG) at Syowa Station, Antarctica in 1998 [Nawa et al. 1998], and then were confirmed at various sites. Other unknown slightly broad spectrum peaks were also found as streak on spectrogram in seismic normal mode band of Syowa SG data. But these signals ware not found in gravimeter and seismometer records from any other s...
Review of Applications of Nonlinear Normal Modes for Vibrating Mechanical Systems
Avramov, Konstantin; Mikhlin, Yuri
2013-01-01
International audience This paper is an extension of the previous review Nonlinear Normal Modes for Vibrating Mechanical Systems. Review of Theoretical Developments done by the authors, and it is devoted to applications of nonlinear normal modes (NNMs) theory. NNMs are typical regimes of motions in wide classes of nonlinear mechanical systems. The significance of NNMs for mechanical engineering is determined by several important properties of these motions. Forced resonances motions of non...
Castello-Branco, K H
2003-01-01
We consider perturbations of Schwarzschild-de Sitter (SdS) black holes. Following the analysis performed by Motl and Neitzke, we analytically study the perturbation equation continued to the complex plane and compute the associated monodromy. We show that the SdS case has features similar to those of asymptotically flat Schwarzschild and deduce an analytic expression for the asymptotic, highly damped quasi-normal mode spectrum. For the case of near-extreme SdS black holes our results are qualitatively supported by very recent numerical data.
Sibaev, M; Crittenden, D L
2016-06-01
In this paper, we outline a general, scalable, and black-box approach for calculating high-order strongly coupled force fields in rectilinear normal mode coordinates, based upon constructing low order expansions in curvilinear coordinates with naturally limited mode-mode coupling, and then transforming between coordinate sets analytically. The optimal balance between accuracy and efficiency is achieved by transforming from 3 mode representation quartic force fields in curvilinear normal mode coordinates to 4 mode representation sextic force fields in rectilinear normal modes. Using this reduced mode-representation strategy introduces an error of only 1 cm(-1) in fundamental frequencies, on average, across a sizable test set of molecules. We demonstrate that if it is feasible to generate an initial semi-quartic force field in curvilinear normal mode coordinates from ab initio data, then the subsequent coordinate transformation procedure will be relatively fast with modest memory demands. This procedure facilitates solving the nuclear vibrational problem, as all required integrals can be evaluated analytically. Our coordinate transformation code is implemented within the extensible PyPES library program package, at http://sourceforge.net/projects/pypes-lib-ext/. PMID:27276945
Sini, R; Kuriakose, V C
2008-01-01
Dirac equation for a general black hole metric having a cosmic string in the back ground is derived. We evaluate quasi normal mode frequencies for Schwarzschild, RN extremal, SdS and near extremal SdS black hole space times with cosmic string perturbed by a massless Dirac field, using WKB approximation.
Normal mode approach to modelling of feedback stabilization of the resistive wall mode
Feedback stabilization of the resistive wall mode (RWM) of a plasma in a general feedback configuration is formulated in terms of the normal modes of the plasma-resistive wall system. The growth/damping rates and the eigenfunctions of the normal modes are determined by an extended energy principle for the plasma during its open (feedback) loop operation. A set of equations are derived for the time evolution of these normal modes with currents in the feedback coils. The dynamics of the feedback system is completed by the prescription of the feedback logic. The feasibility of the feedback is evaluated by using the Nyquist diagram method or by solving the characteristic equations. The elements of the characteristic equations are formed from the growth and damping rates of the normal modes, the sensor matrix of the perturbation fluxes detected by the sensor loops, the excitation matrix of the energy input to the normal modes by the external feedback coils, and the feedback logic. (The RWM is also predicted to be excited by an external error field to a large amplitude when it is close to marginal stability.) This formulation has been implemented numerically and applied to the DIII-D tokamak. It is found that feedback with poloidal sensors is much more effective than feedback with radial sensors. Using radial sensors, increasing the number of feedback coils from a central band on the outboard side to include an upper and a lower band can substantially increase the effectiveness of the feedback system. The strength of the RWM that can be stabilized is increased from γτw = 1 to 30 (γ is the growth rate of the RWM in the absence of feedback and τw is the resistive wall time constant) Using poloidal sensors, just one central band of feedback coils is sufficient for the stabilization of the RWM with γτw = 30. (author)
Ehrhardt, David A.; Allen, Matthew S.
2016-08-01
Nonlinear Normal Modes (NNMs) offer tremendous insight into the dynamic behavior of a nonlinear system, extending many concepts that are familiar in linear modal analysis. Hence there is interest in developing methods to experimentally and numerically determine a system's NNMs for model updating or simply to characterize its dynamic response. Previous experimental work has shown that a mono-harmonic excitation can be used to isolate a system's dynamic response in the neighborhood of a NNM along the main backbones of a system. This work shows that a multi-harmonic excitation is needed to isolate a NNM when well separated linear modes of a structure couple to produce an internal resonance. It is shown that one can tune the multiple harmonics of the input excitation using a plot of the input force versus the response velocity until the area enclosed by the force-velocity curve is minimized. Once an appropriated NNM is measured, one can increase the force level and retune the frequency to obtain a NNM at a higher amplitude or remove the excitation and measure the structure's decay down a NNM backbone. This work explores both methods using simulations and measurements of a nominally-flat clamped-clamped beam excited at a single point with a magnetic force. Numerical simulations are used to validate the method in a well defined environment and to provide comparison with the experimentally measured NNMs. The experimental results seem to produce a good estimate of two NNMs along their backbone and part of an internal resonance branch. Full-field measurements are then used to further explore the couplings between the underlying linear modes along the identified NNMs.
Salby, M. L.
1981-01-01
An investigation is conducted regarding the influence of mean field variations on the realization of planetary normal modes, taking into account the mode response and structure in the presence of simple background nonuniformities. It is found that mean field variations have the combined effect of depressing, shifting, and broadening the characteristic response of Rossby normal modes. While nonuniformities in both the mean wind and temperature fields contribute to the reduction in peak response, the former are primarily responsible for translation and spectral broadening. An investigation is conducted to determine which modes may be realized in actual atmospheric configurations and which may be identified. For both the equinox and solstice configurations, response peaks corresponding to all of the first four modes of wavenumbers 1, 2, and 3 are readily visible above the noise.
Iron normal mode dynamics in a porphyrin-imidazole model for deoxyheme proteins
Iron vibrational modes of a deoxyheme protein model (2-methylimidazole)(tetraphenylporphinato)iron(II), [Fe(TPP)(2-MeImH)], have been studied by refining normal mode calculations to nuclear resonance vibrational spectroscopy (NRVS) data. The NRVS measurements give quantitative frequencies and iron amplitudes of all modes with significant Fe vibrational motion. Modes with in-plane displacement of iron are distinguished from those involving out-of-plane motion by measurements on oriented single-crystal samples. Normal modes having large overlaps with in-plane ν42, ν50, and ν53 modes of the porphyrin core are identified, as well as several modes with large iron-imidazole stretch components. An out-of-plane mode at 78 cm-1 shows significant doming of the porphyrin core, but the largest Fe doming motion arises from the coupling of phenyls and imidazole at 25 cm-1
Normal mode Rossby waves and their effects on chemical composition in the late summer stratosphere
Pendlebury, D.; Shepherd, T. G.; Pritchard, M. S.; C. McLandress
2008-01-01
During past MANTRA campaigns, ground-based measurements of several long-lived chemical species have revealed quasi-periodic fluctuations on time scales of several days. These fluctuations could confound efforts to detect long-term trends from MANTRA, and need to be understood and accounted for. Using the Canadian Middle Atmosphere Model, we investigate the role of dynamical variability in the late summer stratosphere due to normal mode Rossby waves and the impact of this variability on fluctu...
Normal mode Rossby waves and their effects on chemical composition in the late summer stratosphere
Pendlebury, D.; Shepherd, T. G.; M. Pritchard; C. McLandress
2008-01-01
During past MANTRA campaigns, ground-based measurements of several long-lived chemical species have revealed quasi-periodic fluctuations on time scales of several days. These fluctuations could confound efforts to detect long-term trends from MANTRA, and need to be understood and accounted for. Using the Canadian Middle Atmosphere Model, we investigate the role of dynamical variability in the late summer stratosphere due to normal mode Rossby waves and the impact of this vari...
Nonlinear Normal Modes of a Rotating Shaft Based on the Invariant Manifold Method
Mathias Legrand; Dongying Jiang; Christophe Pierre; Shaw, Steven W.
2002-01-01
International audience The nonlinear normal mode methodology is generalized to the study of a rotating shaft supported by two short journal bearings. For rotating shafts, nonlinearities are generated by forces arising from the supporting hydraulic bearings. In this study, the rotating shaft is represented by a linear beam, while a simplified bearing model is employed so that the nonlinear supporting forces can be expressed analytically. The equations of motion of the coupled shaft-bearings...
Eslambolchi, Hossein
1984-01-01
It is well known that normal mode coupling in large diameter piezoelectric plates causes serious difficulties when attempting to operate over wide frequency bands. As a consequence transducers are commonly constructed as a mosaic of elemental resonators, each of which has a predominant single mode of mechanical oscillation at the frequency of interest. Such transducer arrays may be electrically steered to angles other than normal by applying different phases of driving voltages to different e...
Black Boles in the 3D Higher Spin Theory and Their Quasi Normal Modes
Cabo-Bizet, Alejandro; Giraldo-Rivera, V I; Narain, K S
2014-01-01
We present a class of 3D Black Holes based on flat connections which are polynomials in the BTZ $hs(\\lambda)\\times hs(\\lambda)$-valued connection. We solve analytically the fluctuation equations of matter in their background and find the spectrum of their Quasi Normal Modes. We analyze the bulk to boundary two-point functions. We also relate our results and those arising in other backgrounds discussed recently in the literature on the subject.
Normal Modes of Vibration of Mixed KBr/RbBr Crystals
Normal modes of vibration of crystals of KBr/RbBr containing 50 and 20 at. % of RbBr have been compared by neutron scattering with normal modes in KBr. In both the 20 and 50% crystals, normal modes were well defined. For the [111] LA branch, the decrease in frequency in going from pure KBr to both mixed crystals exhibited a dependence on wave vector characteristic of a resonance mode of frequency approximately 2.1 (1012 cps). The widths of the neutron groups were larger in the resonance region. Other modes did not show resonance behaviour. The frequencies of the [111] TA, [111] TO and [110] TA branches in the 50% crystal were less than those in KBr by an approximately constant small amount; the shifts are 0.11±0.06, 0.5±0.1 and 0.16±0.04(1012cps) respectively. There were no appreciable increases in the widths of the neutron groups from these modes. These results are compared with theoretical calculations based on mass defects from the mean lattice approximation. (author)
Generalization of the singular normal mode method for isothermal irreversible Vlasov systems
Irreversible Vlasov systems, i.e. systems governed by a Vlasov-type kinetic equation including entropy-producing collision terms, are treated by the techniques of singular normal modes and singular integral equations using a new indirect method which renders possible a straightforward generalization of the Case formalism as developed originally for collision-free Vlasov plasmas. This method is in contrast to a more complex method given by the present authors for the first application of the singular normal mode expansion to irreversible Vlasov systems (1970). The linearized Vlasov operator supplemented by complete Bhatnagar-Gross-Krook collision integrals as the most important model collision terms is analyzed in detail for a nonrelativistic, nondegenerate, stationary electron gas with neutralizing positive ions and neutral particles without a magnetic field at constant temperature, generalizations for more complex irreversible Vlasov systems being possible. The key of the indirect method given is the introduction of a transformed electron distribution function containing as an additive term an integral over the usual distribution function. The new kinetic equation and its adjoint equation become again linear integral equations and yield a set of regular and singular normal modes which are proved to be orthogonal and complete. The initial value problem is solved exactly. A comparison is made with the Laplace transform theory of Landau which for the full Vlasov-BGK equation is recast into a compact form. The time-behaviour of the solutions is discussed. (author)
It is known that the nonstrictly thermal character of the Hawking radiation spectrum harmonizes Hawking radiation with black hole (BH) quasi-normal modes (QNM). This paramount issue has been recently analyzed in the framework of both Schwarzschild BHs (SBH) and Kerr BHs (KBH). In this assignment, we generalize the analysis to the framework of nonextremal Reissner-Nordström BHs (RNBH). Such a generalization is important because in both Schwarzschild and Kerr BHs an absorbed (emitted) particle has only mass. Instead, in RNBH the particle has charge as well as mass. In doing so, we expose that, for the RNBH, QNMs can be naturally interpreted in terms of quantum levels for both particle emission and absorption. Conjointly, we generalize some concepts concerning the RNBH's “effective states.”
Soto, C A Téllez; Costa, A C; Versiane, O; Lemma, T; Machado, N C F; Mondragón, M A; Martin, A A
2015-07-01
Theoretical and experimental bands have been assigned to the Fourier Transform Infrared (FT-IR) and FT-Raman spectra of the bis(diethyldithiocarbamate)Cd(II) complex, abbreviated as ([Cd(DDTC)2]). The calculations and spectral interpretation have been based on the DFT/B3LYP method, infrared and Raman second derivative spectra, and band deconvolution analysis to assist in the assignment of observed fundamentals. This study validated the unusual pseudo tetrahedral molecular structure formed around the Cd(II) cation. Surface-enhanced Raman scattering (SERS) was used to determine the interactions of the normal-modes of the diethyldithiocarbamate cadmium (II) complex on nano-structured silver surfaces. Natural bond orbital (NBO) analysis was also carried out to study the Cd(II) hybridization causing the pseudo tetrahedral geometry of the framework of the [Cd(DDTC)2] complex, and to confirm the charge transfer mechanisms through second order perturbation theory analysis of the Fox Matrix. In order to find out the electronic dispersion of the Mulliken atomic charges (MAC) in the normal modes, we calculated the MAC for each normal mode and correlated these values with the SERS effect. Experimental UV-Vis spectra were obtained and charge transfer bands were assigned. Good agreement between the calculated and experimental values for the vibrational and UV-Vis spectra was obtained. PMID:25813176
Téllez Soto, C. A.; Costa, A. C.; Versiane, O.; Lemma, T.; Machado, N. C. F.; Mondragón, M. A.; Martin, A. A.
2015-07-01
Theoretical and experimental bands have been assigned to the Fourier Transform Infrared (FT-IR) and FT-Raman spectra of the bis(diethyldithiocarbamate)Cd(II) complex, abbreviated as ([Cd(DDTC)2]). The calculations and spectral interpretation have been based on the DFT/B3LYP method, infrared and Raman second derivative spectra, and band deconvolution analysis to assist in the assignment of observed fundamentals. This study validated the unusual pseudo tetrahedral molecular structure formed around the Cd(II) cation. Surface-enhanced Raman scattering (SERS) was used to determine the interactions of the normal-modes of the diethyldithiocarbamate cadmium (II) complex on nano-structured silver surfaces. Natural bond orbital (NBO) analysis was also carried out to study the Cd(II) hybridization causing the pseudo tetrahedral geometry of the framework of the [Cd(DDTC)2] complex, and to confirm the charge transfer mechanisms through second order perturbation theory analysis of the Fox Matrix. In order to find out the electronic dispersion of the Mulliken atomic charges (MAC) in the normal modes, we calculated the MAC for each normal mode and correlated these values with the SERS effect. Experimental UV-Vis spectra were obtained and charge transfer bands were assigned. Good agreement between the calculated and experimental values for the vibrational and UV-Vis spectra was obtained.
Nagy, Tibor; Vikár, Anna; Lendvay, György, E-mail: lendvay.gyorgy@ttk.mta.hu [Institute of Materials and Environmental Chemistry, Research Centre for Natural Sciences, Hungarian Academy of Sciences, Magyar tudósok körútja 2., H-1117 Budapest (Hungary)
2016-01-07
The quasiclassical trajectory (QCT) method is an efficient and important tool for studying the dynamics of bimolecular reactions. In this method, the motion of the atoms is simulated classically, and the only quantum effect considered is that the initial vibrational states of reactant molecules are semiclassically quantized. A sensible expectation is that the initial ensemble of classical molecular states generated this way should be stationary, similarly to the quantum state it is supposed to represent. The most widely used method for sampling the vibrational phase space of polyatomic molecules is based on the normal mode approximation. In the present work, it is demonstrated that normal mode sampling provides a nonstationary ensemble even for a simple molecule like methane, because real potential energy surfaces are anharmonic in the reactant domain. The consequences were investigated for reaction CH{sub 4} + H → CH{sub 3} + H{sub 2} and its various isotopologs and were found to be dramatic. Reaction probabilities and cross sections obtained from QCT calculations oscillate periodically as a function of the initial distance of the colliding partners and the excitation functions are erratic. The reason is that in the nonstationary ensemble of initial states, the mean bond length of the breaking C–H bond oscillates in time with the frequency of the symmetric stretch mode. We propose a simple method, one-period averaging, in which reactivity parameters are calculated by averaging over an entire period of the mean C–H bond length oscillation, which removes the observed artifacts and provides the physically most reasonable reaction probabilities and cross sections when the initial conditions for QCT calculations are generated by normal mode sampling.
Nagy, Tibor; Vikár, Anna; Lendvay, György
2016-01-01
The quasiclassical trajectory (QCT) method is an efficient and important tool for studying the dynamics of bimolecular reactions. In this method, the motion of the atoms is simulated classically, and the only quantum effect considered is that the initial vibrational states of reactant molecules are semiclassically quantized. A sensible expectation is that the initial ensemble of classical molecular states generated this way should be stationary, similarly to the quantum state it is supposed to represent. The most widely used method for sampling the vibrational phase space of polyatomic molecules is based on the normal mode approximation. In the present work, it is demonstrated that normal mode sampling provides a nonstationary ensemble even for a simple molecule like methane, because real potential energy surfaces are anharmonic in the reactant domain. The consequences were investigated for reaction CH4 + H → CH3 + H2 and its various isotopologs and were found to be dramatic. Reaction probabilities and cross sections obtained from QCT calculations oscillate periodically as a function of the initial distance of the colliding partners and the excitation functions are erratic. The reason is that in the nonstationary ensemble of initial states, the mean bond length of the breaking C-H bond oscillates in time with the frequency of the symmetric stretch mode. We propose a simple method, one-period averaging, in which reactivity parameters are calculated by averaging over an entire period of the mean C-H bond length oscillation, which removes the observed artifacts and provides the physically most reasonable reaction probabilities and cross sections when the initial conditions for QCT calculations are generated by normal mode sampling. PMID:26747798
Normal mode calculation for triple helical DNA, stability and hydration effects
Dadarlat, Voichita Maria
The effective field model for the dynamics of the triple helix d(T)n - d(A)n - d(T)n DNA polymer in solution has been applied to determine the vibrational normal modes of the system for both A and B conformation. The effect of site-bound counterions as compared to the area-bound counterions has been considered specifically by explicitly introducing degrees of freedom for the three counterions associated with a unit cell and coupling these to the DNA degrees of freedom via appropriate interactions. Stability of the system for all vibrational modes (positive eigenvalues for the solution of the dynamics problem) was used as a criterion to find possible equilibrium positions of the site-bound counterions in specific conditions of weak covalent bonding between the counterions and the phosphate free oxygens and distance dependent dielectric constants. Normal mode calculation for the A conformation shows that this type of triple helix is not stable in aqueous solutions unless the counterions are site-bound in certain positions close to the phosphate groups. The equilibrium domains for the positions of the counterions in both conformations have been determined. Free energy calculations for the two triple helices show that the B conformation is more stable than the A conformation. Our calculated normal modes match reasonably well with the experimental IR spectra. The effect of adding structural waters to the triplex DNA in the B conformation have been studied. The results clearly show that there is an inverse proportional relationship between the degree of boundness of the water molecules to the atoms in the triple helix and the relative humidity (RH) of the samples.
The quasiclassical trajectory (QCT) method is an efficient and important tool for studying the dynamics of bimolecular reactions. In this method, the motion of the atoms is simulated classically, and the only quantum effect considered is that the initial vibrational states of reactant molecules are semiclassically quantized. A sensible expectation is that the initial ensemble of classical molecular states generated this way should be stationary, similarly to the quantum state it is supposed to represent. The most widely used method for sampling the vibrational phase space of polyatomic molecules is based on the normal mode approximation. In the present work, it is demonstrated that normal mode sampling provides a nonstationary ensemble even for a simple molecule like methane, because real potential energy surfaces are anharmonic in the reactant domain. The consequences were investigated for reaction CH4 + H → CH3 + H2 and its various isotopologs and were found to be dramatic. Reaction probabilities and cross sections obtained from QCT calculations oscillate periodically as a function of the initial distance of the colliding partners and the excitation functions are erratic. The reason is that in the nonstationary ensemble of initial states, the mean bond length of the breaking C–H bond oscillates in time with the frequency of the symmetric stretch mode. We propose a simple method, one-period averaging, in which reactivity parameters are calculated by averaging over an entire period of the mean C–H bond length oscillation, which removes the observed artifacts and provides the physically most reasonable reaction probabilities and cross sections when the initial conditions for QCT calculations are generated by normal mode sampling
Unstable normal mode for Rayleigh--Taylor instability in viscous fluids
The character of the growth rates of the normal modes for Rayleigh--Taylor instability of superposed incompressible, viscous fluids is analyzed in terms of appropriately scaled dimensionless parameters and a particularly simple representation of the Rayleigh--Taylor dispersion relation. The chief feature that emerges is that the scaled growth rate is remarkably insensitive to the values of fluid densities and viscosities. To within a few percent, the physical growth rate depends only on the surface tension, the density-weighted average viscosity, and the effective acceleration. Approximate formulae for the most unstable wavenumber and the corresponding maximum growth rate are given
Pump induced normal mode splittings in phase conjugation in a Kerr nonlinear waveguide
S Dutta Gupta
2000-03-01
Phase conjugation in a Kerr nonlinear waveguide is studied with counter-propagating normally incident pumps and a probe beam at an arbitrary angle of incidence. Detailed numerical results for the specular and phase conjugated reﬂectivities are obtained with full account of pump depletion. For sufﬁcient strengths of the pump a normal mode splitting is demonstrated in both the specular and the phase conjugated reﬂectivities of the probe wave. The splitting is explained in terms of a simple model under undepleted pump approximation.
Quasi-normal mode approach to the local-field problem in quantum optics
Ge, Rong-Chun; Young, Jeff F.; Hughes, S
2015-01-01
The local-field (LF) problem of a finite-size dipole emit- ter radiating inside a lossy inhomogeneous structure is a long-standing and challenging quantum optical problem, and it now is becoming more important due to rapid advances in solid-state fabrication technologies. Here we introduce a simple and accurate quasi-normal mode (QNM) technique to solve this problem analyti- cally by separating the scattering problem into contribu- tions from the QNM and an image dipole. Using a real- cavity ...
DNA-triplex conformation from normal mode and hydrogen bond stability calculations.
Chen, Y. Z.; Prohofsky, E. W.; Powell, J. W.; White, A. P.
1996-03-01
Triple-stranded DNAs are of potential applications in genome mapping and in the treatment of genetic disorders with little side-effect. Despite significant interests, structural information of DNA triplexes is limited and sometimes conflicting. For instance, two structural models with different conformation have been proposed for a DNA-triplex Poly(dA)\\cdot2Poly(dT). We propose that the sensitivity of normal modes and hydrogen-bond stability on conformation can be used to determine the structure of biomolecules difficult to access by other methods. The structural model representative of the true conformation should have normal modes in agreement with observations, and have most stable hydrogen bonds which melt at observed temperatures. We carried out calculations on the two models of Poly(dA)\\cdot2Poly(dT) and found that one model is consistent with observations at high humidity and thus most likely a good approximation to the true conformation in that environment. Our method has potential application in structural prediction for other biomolecules.
Rai, Brajesh K; Durbin, Stephen M.; Prohofsky, Earl W.; Sage, J. Timothy; Wyllie, Graeme R. A.; Scheidt, W. Robert; Sturhahn, Wolfgang; Alp, E. Ercan
2002-01-01
The complete iron atom vibrational spectrum has been obtained by refinement of normal mode calculations to nuclear inelastic x-ray absorption data from (nitrosyl)iron(II)tetraphenylporphyrin, FeTPP(NO), a useful model for heme dynamics in myoglobin and other heme proteins. Nuclear resonance vibrational spectroscopy (NRVS) provides a direct measurement of the frequency and iron amplitude for all normal modes involving significant displacement of (57)Fe. The NRVS measurements on isotopically en...
Application of integral codes for simulation of WWER type reactor off-normal modes
The article concerns the experience in developing of calculating schemes, formation of input data set and its qualification using simulation of WWER-440 reactor installations off-normal modes by MELCOR-1.8.5 code as an example. Good reproducibility with experimental data is obtained and adequacy of suggested WWER-440 type reactor models to corresponding real installations is confirmed. The acceptability of non-emergency circulation circuit loops merging in calculating model is shown. The necessity of simulation of steam generator tube bundles along length on the first circuit side no less than by three calculating volumes is substantiated. The need of hydraulic lock and surge line simulation in view of three calculating volumes (horizontal and two vertical) is shown. The parameters of communications between calculating volumes are chose on the base of experimental results on corresponding reactor installations or their models
Quasi-normal modes of Schwarzschild-de Sitter black holes
Zhidenko, A
2004-01-01
The low-laying frequencies of characteristic quasi-normal modes (QNM) of Schwarzschild-de Sitter (SdS) black holes have been calculated for fields of different spin using the 6th-order WKB approximation and the approximation by the P"{o}shl-Teller potential. The well-known asymptotic formula for large $l$ is generalized here on a case of the Schwarzchild-de Sitter black hole. In the limit of the near extreme $L$ term the results given by both methods are in a very good agreement, and in this limit fields of different spin decay with the same rate. In addition, the fact that the spectrum of massless Dirac quasi-normal frequencies is the same for opposite chyrality has been numerically proved for SdS background.
A coupling model for quasi-normal modes of photonic resonators
Vial, Benjamin
2016-01-01
We develop a model for the coupling of quasi-normal modes in open photonic systems consisting of two resonators. By expressing the modes of the coupled system as a linear combination of the modes of the individual particles, we obtain a generalized eigenvalue problem involving small size dense matrices. We apply this technique to a 2D problem of a high index rod dimmer of rectangular cross section for Transverse Electric (TE) polarization. The results of our model are compared with full-wave finite element simulations and show a good agreement for the four lowest eigenvalues by taking into account the two lowest eigenfrequencies of the isolated rods. This model provides interesting physical insights on the coupling scheme at stake in such systems and pave the way for the design and optimization of resonances in more complicated systems, including the engineering of metamaterial unit cells.
Cavity cooling and normal-mode spectroscopy of a bound atom-cavity system
Full text: Single atoms strongly coupled to the field of an optical cavity form an attractive system for the realization of an atom-light interface useful for quantum information protocols. An experimental implementation of these schemes requires atoms which are trapped, cooled and localized in the cavity mode at a region of strong coupling. In the experiment presented here, single atoms are trapped and stored in a far-detuned intracavity dipole trap. We demonstrate cavity cooling by illuminating the system with a weak, slightly blue-detuned light beam. This extends the storage time of an atom, which is limited by parametric heating from fluctuations of the intracavity dipole trap, by more than a factor of two. The observed cooling force is of Sisyphus-type and was predicted. A special feature of this force is that it does not rely on the spontaneous emission of a photon by the atom, and therefore the cooling force is at least five times larger than the force achievable for free-space cooling methods with comparable excitation of a two-level atom. Preparing single atoms strongly-coupled to the mode of a high-finesse cavity in this way, we observe two well-resolved normal-mode peaks both in transmission of the cavity as well as in the trap lifetime. The experimental data agree well with a Monte Carlo simulation, demonstrating the localization of the atom to within a tenth of a wavelength at a cavity antinode. The ability to individually excite the normal modes of a bound atom-cavity system shows that we have reached good control over this fundamental quantum system. (author)
随机浅海声传播简正波起伏%Normal mode fluctuation of sound propagating in random shallow water
彭临慧; 王桂波
2006-01-01
Research of fluctuation of sound propagation in a random shallow water environment is of great interest in predicting sound field and environmental parameters for random ocean investigation and monitoring. This paper studies the normal mode fluctuation of sound propagation in random shallow water. Monte Carlo simulation is used to analyze the sound field fluctuation induced by sound speeds random fluctuation with Dozier's statistical coupled mode equations in a random ocean. The random sound speed model is derived based on the statistic analysis of a temperature chain data in shallow sea. The results show that the amplitude fluctuation of normal mode induced by sound speed random fluctuation is larger than the amplitude fluctuation of sound pressure. If the source position is close to the sensitive depth of a normal mode, the scintillation index of this normal mode would be 2～3 order of magnitude larger than the variance of normal mode amplitude fluctuation. As such, the scintillation index of normal mode is an important parameter for detecting sound propagating fluctuation. This article reveals that variance of the sound pressure fluctuation is linear against distance, variance of normal mode amplitude fluctuation, and modal scintillation index.%随机浅海环境中声传播起伏的研究,对于随机海洋环境声场预报及海洋环境参数反演和遥测都有十分重要的意义.文中对随机浅海中声传播的简正波起伏进行了研究,利用L.B.Dozier统计耦合模式方程,通过Monte Carlo数值模拟分析声速场随机变化所产生的声场起伏规律.随机声速场模型由海上温度链测量数据统计规律分析得到.结果表明,声速场随机起伏所导致的简正波幅度起伏远高于声压的起伏;当声源处在某一阶简正波的敏感深度位置时,该阶简正波的闪烁系数会比简正波幅度起伏方差高2～3个量级;在所分析随机声速场模型下,声压起伏方差、简正波幅度起伏
Žagar, N.; Kasahara, A.; Terasaki, K.; Tribbia, J.; Tanaka, H.
2015-04-01
This article presents new software for the analysis of global dynamical fields in (re)analyses, weather forecasts and climate models. A new diagnostic tool, developed within the MODES project, allows one to diagnose properties of balanced and inertio-gravity (IG) circulations across many scales. In particular, the IG spectrum, which has only recently become observable, can be studied simultaneously in the mass and wind fields while considering the whole model depth in contrast to the majority of studies. The paper includes the theory of normal-mode function (NMF) expansion, technical details of the Fortran 90 code, examples of namelists which control the software execution and outputs of the software application on the ERA Interim reanalysis data set. The applied libraries and default compiler are from the open-source domain. A limited understanding of Fortran suffices for the successful implementation of the software. The presented application of the software to the ERA Interim data set reveals several aspects of the large-scale circulation after it has been partitioned into the linearly balanced and IG components. The global energy distribution is dominated by the balanced energy while the IG modes contribute around 10% of the total wave energy. However, on sub-synoptic scales, IG energy dominates and it is associated with the main features of tropical variability on all scales. The presented energy distribution and features of the zonally averaged and equatorial circulation provide a reference for the validation of climate models.
Žagar, N.; Kasahara, A.; Terasaki, K.; Tribbia, J.; Tanaka, H.
2014-12-01
The paper presents new software for the analysis of global dynamical fields in (re)analyses, weather forecasts and climate models. A new diagnostic tool, developed within the MODES project, allows one to diagnose properties of balanced and inertio-gravity (IG) circulation across many scales. In particular, the IG spectrum, which has only recently become observable, can be studied simultaneously in the mass field and wind field and considering the whole model depth in contrary to majority of studies. The paper presentation includes the theory of normal-mode function expansion, technical details of the Fortran 90 code, examples of namelists which control the software execution and outputs of the software application on the reanalysis dataset ERA Interim. The applied libraries and default compiler are from the open-source domain. A limited understanding of Fortran suffices for the successful implementation of the software. The presented application of the software to the ERA Interim dataset show some features of the large-scale circulation after it has been split into the balanced and IG components. The global energy distribution is dominated by the balanced energy with IG modes making less than 10% of the total wave energy. However, on subsynoptic scales IG energy dominates and it is associated with the main features of tropical variability on all scales. The presented energy distribution and features of the zonally-averaged and equatorial circulation provide a reference for the validation of climate models.
Emílio Borges
2007-04-01
Full Text Available A simple method to obtain molecular Cartesian coordinates as a function of vibrational normal modes is presented in this work. The method does not require the definition of special matrices, like the F and G of Wilson, neither of group theory. The Eckart's conditions together with the diagonalization of kinetic and potential energy are the only required expressions. This makes the present approach appropriate to be used as a preliminary study for more advanced concepts concerning vibrational analysis. Examples are given for diatomic and triatomic molecules.
Normal mode Rossby waves and their effects on chemical composition in the late summer stratosphere
Pendlebury, D.; Shepherd, T. G.; Pritchard, M.; McLandress, C.
2008-04-01
During past MANTRA campaigns, ground-based measurements of several long-lived chemical species have revealed quasi-periodic fluctuations on time scales of several days. These fluctuations could confound efforts to detect long-term trends from MANTRA, and need to be understood and accounted for. Using the Canadian Middle Atmosphere Model, we investigate the role of dynamical variability in the late summer stratosphere due to normal mode Rossby waves and the impact of this variability on fluctuations in chemical species. Zonal wavenumber 1, westward travelling waves are considered with average periods of 5, 10 and 16 days. Time-lagged correlations between the temperature and nitrous oxide, methane and ozone fields are calculated in order to assess the possible impact of these waves on the chemical species. Using Fourier-wavelet decomposition and correlating the fluctuations between the temperature and chemical fields, we determine that variations in the chemical species are well-correlated with the 5- and 10-day waves between 30 and 60 km, although the nature of the correlations depend strongly on altitude. Interannual variability of the waves is also examined.
Normal mode Rossby waves and their effects on chemical composition in the late summer stratosphere
D. Pendlebury
2008-04-01
Full Text Available During past MANTRA campaigns, ground-based measurements of several long-lived chemical species have revealed quasi-periodic fluctuations on time scales of several days. These fluctuations could confound efforts to detect long-term trends from MANTRA, and need to be understood and accounted for. Using the Canadian Middle Atmosphere Model, we investigate the role of dynamical variability in the late summer stratosphere due to normal mode Rossby waves and the impact of this variability on fluctuations in chemical species. Zonal wavenumber 1, westward travelling waves are considered with average periods of 5, 10 and 16 days. Time-lagged correlations between the temperature and nitrous oxide, methane and ozone fields are calculated in order to assess the possible impact of these waves on the chemical species. Using Fourier-wavelet decomposition and correlating the fluctuations between the temperature and chemical fields, we determine that variations in the chemical species are well-correlated with the 5- and 10-day waves between 30 and 60 km, although the nature of the correlations depend strongly on altitude. Interannual variability of the waves is also examined.
Normal mode Rossby waves and their effects on chemical composition in the late summer stratosphere
D. Pendlebury
2007-08-01
Full Text Available During past MANTRA campaigns, ground-based measurements of several long-lived chemical species have revealed quasi-periodic fluctuations on time scales of several days. These fluctuations could confound efforts to detect long-term trends from MANTRA, and need to be understood and accounted for. Using the Canadian Middle Atmosphere Model, we investigate the role of dynamical variability in the late summer stratosphere due to normal mode Rossby waves and the impact of this variability on fluctuations in chemical species. Wavenumber~1, westward travelling waves are considered with average periods of 5, 10 and 16 days. Time-lagged correlations between the temperature and nitrous oxide, methane and ozone fields are calculated in order to assess the possible impact of these waves on the chemical species, although transport may be the dominant effect. Using Fourier-wavelet decomposition and correlating the fluctuations between the temperature and chemical fields, we determine that variations in the chemical species are well-correlated with the 5-day wave and the 10-day wave between 30 and 60 km. Interannual variability of the waves is also examined.
Exact quasi-normal modes for the near horizon Kerr metric
Cvetic, M
2013-01-01
We study the quasi-normal modes of a massless scalar field in a general sub-extreme Kerr back- ground by exploiting the hidden SL(2, R) x SL(2, R) x SO(3) symmetry of the subtracted geometry approximation. This faithfully models the near horizon geometry but locates the black hole in a confining asymptotically conical box analogous to the anti-de-Sitter backgrounds used in string the- ory. There are just two series of modes, given in terms of hypergeometric functions and spherical harmonics, reminiscent of the left-moving and right-moving degrees in string theory: one is over- damped, the other is underdamped and exhibits rotational splitting. The remarkably simple exact formulae for the complex frequencies would in principle allow the determination of the mass and angular momentum from observations of a black hole. No black hole bomb is possible because the Killing field which co-rotates with the horizon is everywhere timelike outside the black hole.
Second Order Quasi-Normal Mode of the Schwarzschild Black Hole
Nakano, Hiroyuki
2007-01-01
We formulate and calculate the second order quasi-normal modes (QNMs) of a Schwarzschild black hole (BH). Gravitational wave (GW) from a distorted BH, so called ringdown, is well understood as QNMs in general relativity. Since QNMs from binary BH mergers will be detected with high signal-to-noise ratio by GW detectors, it is also possible to detect the second perturbative order of QNMs, generated by nonlinear gravitational interaction near the BH. In the BH perturbation approach, we derive the master Zerilli equation for the metric perturbation to second order and explicitly regularize it at the horizon and spatial infinity. We numerically solve the second order Zerilli equation by implementing the modified Leaver's continued fraction method. The second order QNM frequencies are found to be twice the first order ones, and the GW amplitude is up to $\\sim 10%$ that of the first order for the binary BH mergers. Since the second order QNMs always exist, we can use their detections (i) to test the nonlinearity of ...
Fourier transform infrared spectra and normal mode analysis of drug molecules: Zidovudine
Jain, Nivedita; Prabhakar, Santosh; Singh, R. A.
2013-03-01
The FTIR spectra of zidovudine molecule have been recorded in the range 4000-400 cm-1. The title compound is used as a drug against AIDS or HIV. The molecular structure, fundamental vibrational frequencies and intensities of vibrational bands are evaluated using density functional theory (DFT) using BLYP, B3LYP, B3PW91 and MPW1PW91 methods with 6-31+G(d,p) standard basis set. Comparison of simulated spectra with the experimental spectrum provides important informations and the ability of the computational method to describe the vibrational modes. These calculations have allowed finding most stable conformational structure of AZT. Calculated results of the title compound indicate that the drug molecule has syn orientation. The glycosidic bond in AZT and a minimum-energy structure in which the glycosy torsion angle χ and torsion angle γ values are consistent with those in the conformation of AZT in the AZT5-triphosphate bound to HIV RT is determined.
Castello-Branco, K. H. C.; Abdalla, E.
2003-01-01
Following the monodromy technique performed by Motl and Neitzke, we consider the analytic determination of the highly damped (asymptotic) quasi-normal modes of small Schwarzschild-de Sitter (SdS) black holes. We comment the result as compared to the recent numerical data of Konoplya and Zhidenko.
Free and forced Rossby normal modes in a rectangular gulf of arbitrary orientation
Graef, Federico
2016-09-01
A free Rossby normal mode in a rectangular gulf of arbitrary orientation is constructed by considering the reflection of a Rossby mode in a channel at the head of the gulf. Therefore, it is the superposition of four Rossby waves in an otherwise unbounded ocean with the same frequency and wavenumbers perpendicular to the gulf axis whose difference is equal to 2mπ/W, where m is a positive integer and W the gulf's width. The lower (or higher) modes with small m (or large m) are oscillatory (evanescent) in the coordinate along the gulf; these are elucidated geometrically. However for oceanographically realistic parameter values, most of the modes are evanescent. When the gulf is forced at the mouth with a single Fourier component, the response is in general an infinite sum of modes that are needed to match the value of the streamfunction at the gulf's entrance. The dominant mode of the response is the resonant one, which corresponds to forcing with a frequency ω and wavenumber normal to the gulf axis η appropriate to a gulf mode: η =- β sin α/(2ω) ± Mπ/W, where α is the angle between the gulf's axis and the eastern direction (+ve clockwise) and M the resonant's mode number. For zonal gulfs ω drops out of the resonance condition. For the special cases η = 0 in which the free surface goes up and down at the mouth with no flow through it, or a flow with a sinusoidal profile, resonant modes can get excited for very specific frequencies (only for non-zonal gulfs in the η = 0 case). The resonant mode is around the annual frequency for a wide range of gulf orientations α ∈ [40°, 130°] or α ∈ [220°, 310°] and gulf widths between 150 and 200 km; these include the Gulf of California and the Adriatic Sea. If η is imaginary, i.e. a flow with an exponential profile, there is no resonance. In general less modes get excited if the gulf is zonally oriented.
Joint inversion of normal-mode and finite-frequency S-wave data using an irregular tomographic grid
Zaroli, Christophe; Lambotte, Sophie; Lévêque, Jean-Jacques
2015-12-01
Global-scale tomographic models should aim at satisfying the full seismic spectrum. For this purpose, and to better constrain isotropic 3-D variations of shear velocities in the mantle, we tackle a joint inversion of spheroidal normal-mode structure coefficients and multiple-frequency S-wave delay times. In all previous studies for which normal modes were jointly inverted for, with body and/or surface waves, the mantle was laterally parametrized with uniform basis functions, such as spherical harmonics, equal-area blocks and evenly spaced spherical splines. In particular, spherical harmonics naturally appear when considering the Earth's free oscillations. However, progress towards higher resolution joint tomography requires a movement away from such uniform parametrization to overcome its computational inefficiency to adapt to local variations in resolution. The main goal of this study is to include normal modes into a joint inversion based upon a non-uniform parametrization that is adapted to the spatially varying smallest resolving length of the data. Thus, we perform the first joint inversion of normal-mode and body-wave data using an irregular tomographic grid, optimized according to ray density. We show how to compute the projection of 3-D sensitivity kernels for both data sets onto our parametrization made up of spherical layers spanned with irregular Delaunay triangulations. This approach, computationally efficient, allows us to map into the joint model multiscale structural informations from data including periods in the 10-51 s range for body waves and 332-2134 s for normal modes. Tomographic results are focused on the 400-2110 km depth range, where our data coverage is the most relevant. We discuss the potential of a better resolution where the grid is fine, compared to spherical harmonics up to degree 40, as the number of model parameters is similar. Our joint model seems to contain coherent structural components beyond degree 40, such as those related
R., Sini; Varghese, Nijo; Kuriakose, V. C.
2008-01-01
Dirac equation for a general black hole metric having a cosmic string is derived. The quasi-normal mode frequencies for Schwarzschild, RN extremal, SdS and near extremal SdS black hole space-times with cosmic string perturbed by a massless Dirac field are obtained using WKB approximation and found that in all these cases, decay is less in black holes having cosmic string compared to black holes with out string.
The structural model of the unliganded and fully glycosylated simian immunodeficiency virus gp120 core determined to 4.0 Å resolution was substantially improved using a recently developed normal-mode-based anisotropic B-factor refinement method. The envelope protein gp120/gp41 of simian and human immunodeficiency viruses plays a critical role in viral entry into host cells. However, the extraordinarily high structural flexibility and heavy glycosylation of the protein have presented enormous difficulties in the pursuit of high-resolution structural investigation of some of its conformational states. An unliganded and fully glycosylated gp120 core structure was recently determined to 4.0 Å resolution. The rather low data-to-parameter ratio limited refinement efforts in the original structure determination. In this work, refinement of this gp120 core structure was carried out using a normal-mode-based refinement method that has been shown in previous studies to be effective in improving models of a supramolecular complex at 3.42 Å resolution and of a membrane protein at 3.2 Å resolution. By using only the first four nonzero lowest-frequency normal modes to construct the anisotropic thermal parameters, combined with manual adjustments and standard positional refinement using REFMAC5, the structural model of the gp120 core was significantly improved in many aspects, including substantial decreases in R factors, better fitting of several flexible regions in electron-density maps, the addition of five new sugar rings at four glycan chains and an excellent correlation of the B-factor distribution with known structural flexibility. These results further underscore the effectiveness of this normal-mode-based method in improving models of protein and nonprotein components in low-resolution X-ray structures
Capdeville, Y.; Gung, Y.; Romanowicz, B.
2002-12-01
The spectral element method (SEM) has recently been adapted successfully for global spherical earth wave propagation applications. Its advantage is that it provides a way to compute exact seismograms in a 3D earth, without restrictions on the size or wavelength of lateral heterogeneity at any depth, and can handle diffraction and other interactions with major structural boundaries. Its disadvantage is that it is computationally heavy. In order to partly address this drawback, a coupled SEM/normal mode method was developed (Capdeville et al., 2000). This enables us to more efficiently compute bodywave seismograms to realistically short periods (10s or less). In particular, the coupled SEM/normal mode method is a powerful tool to test the validity of some analytical approximations that are currently used in global waveform tomography, and that are considerably faster computationally. Here, we focus on several approximations based on normal mode perturbation theory: the classical "path-average approximation" (PAVA) introduced by Woodhouse and Dziewonski (1984) and well suited for fundamental mode surface waves (1D sensitivity kernels); the non-linear asymptotic coupling theory (NACT), which introduces coupling between mode branches and 2D kernels in the vertical plane containing the source and the receiver (Li and Tanimoto, 1993; Li and Romanowicz, 1995); an extension of NACT which includes out of plane focusing terms computed asymptotically (e.g. Romanowicz, 1987) and introduces 3D kernels; we also consider first order perturbation theory without asymptotic approximations, such as developed for example by Dahlen et al. (2000). We present the results of comparisons of realistic seismograms for different models of heterogeneity, varying the strength and sharpness of the heterogeneity and its location in depth in the mantle. We discuss the consequences of different levels of approximations on our ability to resolve 3D heterogeneity in the earth's mantle.
Al-Attar, D.; Woodhouse, J. H.
2011-12-01
Normal mode spectra provide a valuable data set for global seismic tomography, and, notably, are amongst the few geophysical observables that are sensitive to lateral variations in density structure within the Earth. Nonetheless, the effects of lateral density variations on mode spectra are rather subtle. In order, therefore, to reliably determine density variations with in the earth, it is necessary to make use of sufficiently accurate methods for calculating synthetic mode spectra. In particular, recent work has highlighted the need to perform 'full-coupling calculations' that take into account the interaction of large numbers of spherical earth multiplets. However, present methods for performing such full-coupling calculations require diagonalization of large coupling matrices, and so become computationally inefficient as the number of coupled modes is increased. In order to perform full-coupling calculations more efficiently, we describe a new implementation of the direct solution method for calculating synthetic spectra in laterally heterogeneous earth models. This approach is based on the solution of the inhomogeneous mode coupling equations in the frequency domain, and does not require the diagonalization of large matrices. Early implementations of the direct solution method used LU-decomposition to solve the mode coupling equations. However, as the number of coupled modes is increased, this method becomes impractically slow. To circumvent this problem, we solve the mode coupling equations iteratively using the preconditioned biconjugate gradient algorithm. We present a number of numerical tests to display the accuracy and efficiency of this method for performing large full-coupling calculations. In addition, we describe a frequency-domain formulation of the adjoint method for the calculation of Frechet kernels that show the sensitivity of normal mode observations to variations in earth structure. The calculation of such Frechet kernels involves one solution
Waveform Modeling of 3D Structure of D" Region Using A Coupled SEM/Normal Mode Approach
To, A.; Gung, Y.; Capadeville, Y.; Romanowicz, B.
2003-12-01
The presence of strong lateral heterogeneity in D" is now well documented and presents challenges for seismic modeling. The main challenges are the limited global sampling of D" and the theoretical limits of validity of the present modeling tools, such as standard ray theory and mode approaches. We use coupled normal mode/Spectral Element Method (SEM) to compute synthetic seismograms of Sdiff in the D" part of a tomographic model(SAW24b16, Mégnin and Romanowicz, 2000) down to corner frequency 1/12s. SEM allows to take into account strong heterogeneity in a rigorous manner. The coupled method is much faster than standard SEM, when the numerical part of the computation is restricted to the D" region. In the rest of the mantle, the wave field is computed using efficient normal mode summation. As a first step, we consider a radially symmetric model outside of the D" region, and compare Sdiff synthetics with observed waveforms for a collection of deep earthquakes, for which the effect of strong heterogeneity in the crust and upper mantle is avoided. Observed and synthetic travel time trends are very consistent and in many cases the observed residuals are significantly larger. This indicates that the tomographic model only represents the smooth features of the real structure. Observed waveform amplitudes and SEM synthetics are somewhat less consistent. We compare the predictions for 800 Sdiff phases using SEM with those obtained by more approximate methods : ray theory and NACT (Non-linear asymptotic coupling theory, a normal mode perturbation approach). We discuss systematic trends in the travel times predicted by the different methods, compared to observations. Starting with the tomographic model, and correcting for mantle structure outside of D" using approximate NACT predictions, we next invert for perturbations to the tomographic model, using the coupled SEM/mode computation for the forward part of the modeling, in several regions of D" under the Pacific, which are
Simple illustrations of range-dependence and 3-D effects by normal-mode sound propagation modelling
Ivansson, Sven
2016-01-01
As is well known, the sound-speed profile has significant effects on underwater acoustic sound propagation. These effects can be quantified by normal-mode models, for example. The basic case is a laterally homogeneous medium, for which the sound speed and the density depend on depth only and not on horizontal position. Effects of horizontal medium-parameter variation can be quantified by coupled-mode models, with coupling between mode expansions for laterally homogeneous parts of the medium. In the present paper, these effects are illustrated for media with a particularly simple horizontal parameter variation such that mode shapes do not vary with horizontal position. The modal wavenumbers depend on horizontal position, however. At a vertical interface between regions with laterally homogeneous medium parameters, each mode is reflected as well as transmitted. For the media considered, reflection and transmission coefficients can be computed separately for each mode without mode coupling, and this is done recu...
Rueda, Manuel; Bottegoni, Giovanni; Abagyan, Ruben
2009-03-01
The representation of protein flexibility is still a challenge for the state-of-the-art flexible ligand docking protocols. In this article, we use a large and diverse benchmark to prove that is possible to improve consistently the cross-docking performance against a single receptor conformation, using an equilibrium ensemble of binding site conformers. The benchmark contained 28 proteins, and our method predicted the top-ranked near native ligand poses 20% more efficiently than using a single receptor. The multiple conformations were derived from the collective variable space defined by all heavy-atom elastic network normal modes, including backbone and side chains. We have found that the binding site displacements for best positioning of the ligand seem rather independent from the global collective motions of the protein. We also found that the number of binding site conformations needed to represent nonredundant flexibility was Web site at http://abagyan.scripps.edu/MRC. PMID:19434904
Kumar, Tarun; ManMohan,
2011-01-01
We propose a technique aimed at cooling a harmonically oscillating mirror mechanically coupled to another vibrating mirror to its quantum mechanical ground state. Our method involves optmechanical coupling between two optical cavities. We show that the cooling can be controlled by the mechanical coupling strength between the two movable mirrors, the phase difference between the mechanical modes of the two oscillating mirrors and the photon number in each cavity. We also show that both mechanical and optical cooling can be achieved by transferring energy from one cavity to the other. We also analyze the occurrence of normal-mode splitting (NMS). We find that a hybridization of the two oscillating mirrors with the fluctuations of the two driving optical fields occurs and leads to a splitting of the mechanical and optical fluctuation spectra.
On the computation of long period seismograms in a 3-D earth using normal mode based approximations
Romanowicz, Barbara A.; Panning, Mark P.; Gung, Yuancheng; Capdeville, Yann
2008-11-01
Tomographic inversions for large-scale structure of the earth's mantle involve a forward modelling step of wave propagation through 3-D heterogeneity. Until now, most investigators have worked in the framework of the simplest theoretical assumptions, namely the infinite frequency `ray theory' in the case of body wave traveltime inversions, or the `path-average' approximation (PAVA) to normal mode perturbation theory, in the case of surface waves and long-period waveforms. As interest is shifting to mapping shorter wavelength structures, the need for a more accurate theoretical account of the interaction of seismic waves with mantle heterogeneity, coupled with improvements in path coverage, has been realized. Here we discuss different levels of approximations used in the context of normal mode perturbation theory, when modelling time domain seismic waveforms. We compare the performance of asymptotic approximations, which collapse the effects of 3-D structure onto the great circle vertical plane: the 1-D PAVA and a 2-D approximation called non-linear asymptotic coupling theory (NACT), which both are zeroth order asymptotic approximations. We then discuss how off-vertical plane effects can be introduced using higher order asymptotics. These computationally efficient approximations are compared to the linear Born formalism (BORN), which computes scattering integrals over the entire surface of the sphere. We point out some limitations of this linear formalism in the case of spatially extended anomalies, and show how that can be remedied through the introduction of a non-linear term (NBORN). All these approximations are referenced to a precise 3-D numerical computation afforded by the spectral element method. We discuss simple geometries, and explore a range of sizes of anomalies compared to the wavelength of the seismic waves considered, thus illustrating the range of validity and limitations of the various approximations considered.
Black hole (BH) area quantization may be the key to unlocking a unifying theory of quantum gravity (QG). Surmounting evidence in the field of BH research continues to support a horizon (surface) area with a discrete and uniformly spaced spectrum, but there is still no general agreement on the level spacing. In the specialized and important BH case study, our objective is to report and examine the pertinent groundbreaking work of the strictly thermal and nonstrictly thermal spectrum level spacing of the BH horizon area quantization with included entropy calculations, which aims to tackle this gigantic problem. In particular, such work exemplifies a series of imperative corrections that eventually permits a BH’s horizon area spectrum to be generalized from strictly thermal to nonstrictly thermal with entropy results, thereby capturing multiple preceding developments by launching an effective unification between them. Moreover, the results are significant because quasi-normal modes (QNM) and “effective states” characterize the transitions between the established levels of the nonstrictly thermal spectrum
Corda, Christian
2015-01-01
Some recent important results on black hole (BH) quantum physics concerning the BH effective state and the natural correspondence between Hawking radiation and BH quasi-normal modes (QNMs) are reviewed, clarified and refined. Such a correspondence permits to naturally interpret QNMs as quantum levels in a semi-classical model. This is a model of BH somewhat similar to the historical semi-classical model of the structure of a hydrogen atom introduced by Bohr in 1913. In a certain sense, QNMs represent the "electron" which jumps from a level to another one and the absolute values of the QNMs frequencies "triggered" by emissions (Hawking radiation) and absorption of particles represent the energy "shells" of the "gravitational hydrogen atom". Important consequences on the BH information puzzle are discussed. In fact, it is shown that the time evolution of this "Bohr-like BH model" obeys to a time dependent Schr\\"odinger equation which permits the final BH state to be a pure quantum state instead of a mixed one. ...
Choudhury, T R
2004-01-01
It is known that the imaginary parts of the quasi normal mode (QNM) frequencies for the Schwarzschild black hole are evenly spaced with a spacing that depends only on the surface gravity. On the other hand, for massless minimally coupled scalar fields, there exist no QNMs in the pure DeSitter spacetime. It is not clear what the structure of the QNMs would be for the Schwarzschild-DeSitter (SDS) spacetime, which is characterized by two different surface gravities. We provide a simple derivation of the imaginary parts of the QNM frequencies for the SDS spacetime by calculating the scattering amplitude in the first Born approximation and determining its poles. We find that, for the usual set of boundary conditions in which the incident wave is scattered off the black hole horizon, the imaginary parts of the QNM frequencies have a equally spaced structure with the level spacing depending on the surface gravity of the black hole. However, it is possible to invoke a different boundary condition (in which the incide...
Highlights: ► Geometrical parameters at MP2 level are almost equal to that of B3LYP level. ► Interaction energy and its components are varied linearly with size of the cluster. ► Two scaling factors are applied to account the anharmonic nature of vibrations. ► Excellent agreement between calculated and experimental frequencies is observed. ► Molecular level vibrations provide information of the local hydration environment. - Abstract: We investigate structural, energetic and spectroscopic aspects of the finite size hydrated NO3- · nH2O (n = 1–8) clusters based on the first principles electronic structure calculations. It is observed that the geometrical parameters at MP2/6-311++G(d,p) level are almost equal to that of calculated at B3LYP/6-311++G(d,p) level for the higher size of clusters (n > 3). Our results reveal that total interaction energy and its components do vary linearly with the size of the clusters. Two types of scaling factors are implemented in two different regions to account the effect of anharmonic vibrations. The degeneracy of in-plane bending and asymmetric N-O stretching mode in nitrate system is lifted due to hydration. An excellent agreement is observed between the present calculated H2O bending and asymmetric N-O stretching frequencies with the experimental results (within 4% w.r.t. experimentally measured values). Understanding the nature of normal modes of vibration at the molecular level provides information of the local hydration environment during stepwise solvation.
Sarvesh Kumar Pandey; Prasanta Das; Puspendu K Das; Elangannan Arunan; Sadasivam Manogaran
2015-06-01
It has been shown earlier1 that the relaxed force constants (RFCs) could be used as a measure of bond strength only when the bonds form a part of the complete valence internal coordinates (VIC) basis. However, if the bond is not a part of the complete VIC basis, its RFC is not necessarily a measure of bond strength. Sometimes, it is possible to have a complete VIC basis that does not contain the intramolecular hydrogen bond (IMHB) as part of the basis. This means the RFC of IMHB is not necessarily a measure of bond strength. However, we know that IMHB is a weak bond and hence its RFC has to be a measure of bond strength. We resolve this problem of IMHB not being part of the complete basis by postulating `equivalent’ basis sets where IMHB is part of the basis at least in one of the equivalent sets of VIC. As long as a given IMHB appears in one of the equivalent complete VIC basis sets, its RFC could be used as a measure of bond strength parameter.
de Lasson, Jakob Rosenkrantz; Mørk, Jesper; Kristensen, Philip Trøst
2013-01-01
scatterers in a homogeneous background medium. In addition, we show how several physically important quantities may readily be calculated with the formalism. These quantities include the extinction cross section, the total Green’s tensor, the projected local density of states, and the Purcell factor as well...... as the quasi-normal modes of leaky resonators with the associated resonance frequencies and quality factors. We demonstrate the calculations for the well-known plasmonic dimer consisting of two silver nanoparticles and thus illustrate the versatility of the formalism for use in modeling of advanced...
Prasia, P; Kuriakose, V. C.
2016-01-01
We investigate black holes in a class of dRGT massive gravity for their quasi normal modes (QNMs) for neutral and charged ones using Improved Asymptotic Iteration Method (Improved AIM) and their thermodynamic behavior. The QNMs are studied for different values of the massive parameter m_g for both neutral and charged dRGT black holes under a massless scalar perturbation. As m_g increases, the magnitude of the quasi normal frequencies are found to be increasing. The results are also compared w...
de Lasson, Jakob Rosenkrantz; Kristensen, Philip Trøst; Mørk, Jesper; Gregersen, Niels
2015-01-01
We present and validate a semi-analytical quasi-normal mode (QNM) theory for the local density of states (LDOS) in coupled photonic crystal (PhC) cavity-waveguide structures. By means of an expansion of the Green's function on one or a few QNMs, a closed-form expression for the LDOS is obtained, ......-trivial spectrum with a peak and a dip is found, which is reproduced only when including both the two relevant QNMs in the theory. In both cases, we find relative errors below 1% in the bandwidth of interest.......We present and validate a semi-analytical quasi-normal mode (QNM) theory for the local density of states (LDOS) in coupled photonic crystal (PhC) cavity-waveguide structures. By means of an expansion of the Green's function on one or a few QNMs, a closed-form expression for the LDOS is obtained......, and for two types of two-dimensional PhCs, with one and two cavities side-coupled to an extended waveguide, the theory is validated against numerically exact computations. For the single cavity, a slightly asymmetric spectrum is found, which the QNM theory reproduces, and for two cavities a non...
This paper presents an investigation of a DC glow discharge at low pressure in the normal mode and with Einstein's relation of electron diffusivity. Two-dimensional distributions in Cartesian geometry are presented in the stationary state, including electric potential, electron and ion densities, longitudinal and transverse electrics fields as well as electron temperature. Our results are compared with those obtained in existing literature. The model used in this work is based on the first three moments of Boltzmann's equation. They serve as the continuity equation, the momentum transfer and the energy equations. The set of equations for charged particles presented in monatomic argon gas are coupled in a self-consistent way with Poisson's equation. A parametric study varying the cathode voltage, gas pressure, and secondary electron emission coefficient predicts many of the well-known features of DC discharges. (low temperature plasma)
Prasia, P
2016-01-01
We investigate black holes in a class of dRGT massive gravity for their quasi normal modes (QNMs) for neutral and charged ones using Improved Asymptotic Iteration Method (Improved AIM) and their thermodynamic behavior. The QNMs are studied for different values of the massive parameter m_g for both neutral and charged dRGT black holes under a massless scalar perturbation. As m_g increases, the magnitude of the quasi normal frequencies are found to be increasing. The results are also compared with the Schwarzchild de Sitter (SdS) case. P-V criticallity of the aforesaid black hoels under massles scalar perturbation in the de Sitter space are also studied in this paper. It is found that the thermodynamic behavior of a neutral black hole shows no physically feasible phase transition while a charged black hole shows a definite phase transition.
de Lasson, Jakob Rosenkrantz; Mørk, Jesper; Gregersen, Niels
2015-01-01
We present and validate a semi-analytical quasi-normal mode (QNM) theory for the local density of states (LDOS) in coupled photonic crystal (PhC) cavity-waveguide structures. By means of an expansion of the Green's function on one or a few QNMs, a closed-form expression for the LDOS is obtained, and for two types of two-dimensional PhCs, with one and two cavities side-coupled to an extended waveguide, the theory is validated against numerically exact computations. For the single cavity, a slightly asymmetric spectrum is found, which the QNM theory reproduces, and for two cavities a non-trivial spectrum with a peak and a dip is found, which is reproduced only when including both the two relevant QNMs in the theory. In both cases, we find relative errors below 1% in the bandwidth of interest.
Okal, E. A.
1978-01-01
The theory of the normal modes of the earth is investigated and used to build synthetic seismograms in order to solve source and structural problems. A study is made of the physical properties of spheroidal modes leading to a rational classification. Two problems addressed are the observability of deep isotropic seismic sources and the investigation of the physical properties of the earth in the neighborhood of the Core-Mantle boundary, using SH waves diffracted at the core's surface. Data sets of seismic body and surface waves are used in a search for possible deep lateral heterogeneities in the mantle. In both cases, it is found that seismic data do not require structural differences between oceans and continents to extend deeper than 250 km. In general, differences between oceans and continents are found to be on the same order of magnitude as the intrinsic lateral heterogeneity in the oceanic plate brought about by the aging of the oceanic lithosphere.
Recent theoretical work suggests that violation of the equivalence principle might be revealed in a measurement of the fractional differential acceleration η between two test bodies-of different compositions, falling in the gravitational field of a source mass--if the measurement is made to the level of η≅10-13 or better. This being within the reach of ground based experiments gives them a new impetus. However, while slowly rotating torsion balances in ground laboratories are close to reaching this level, only an experiment performed in a low orbit around the Earth is likely to provide a much better accuracy. We report on the progress made with the 'Galileo Galilei on the ground' (GGG) experiment, which aims to compete with torsion balances using an instrument design also capable of being converted into a much higher sensitivity space test. In the present and following articles (Part I and Part II), we demonstrate that the dynamical response of the GGG differential accelerometer set into supercritical rotation-in particular, its normal modes (Part I) and rejection of common mode effects (Part II)-can be predicted by means of a simple but effective model that embodies all the relevant physics. Analytical solutions are obtained under special limits, which provide the theoretical understanding. A simulation environment is set up, obtaining a quantitative agreement with the available experimental data on the frequencies of the normal modes and on the whirling behavior. This is a needed and reliable tool for controlling and separating perturbative effects from the expected signal, as well as for planning the optimization of the apparatus
Montagner, Jean-Paul; Roult, Genevieve [Institut de Physique du Globe, UMR/CNRS 7154, 4 Place Jussieu, 75252 Paris (France)], E-mail: jpm@ipgp.jussieu.fr
2008-10-15
The free oscillations of the Earth were observed for the first time in the 1960s. They can be divided into spheroidal modes and toroidal modes, which are characterized by three quantum numbers n,l, and m. In a spherically symmetric Earth, the modes are degenerate in m, but the influence of rotation and lateral heterogeneities within the Earth splits the modes and lifts this degeneracy. The occurrence of the Great Sumatra-Andaman earthquake on 24 December 2004 provided unprecedented high-quality seismic data recorded by the broadband stations of the FDSN (Federation of Digital Seismograph Networks). For the first time, it has been possible to observe a very large collection of split modes, not only spheroidal modes but also toroidal modes.
The free oscillations of the Earth were observed for the first time in the 1960s. They can be divided into spheroidal modes and toroidal modes, which are characterized by three quantum numbers n,l, and m. In a spherically symmetric Earth, the modes are degenerate in m, but the influence of rotation and lateral heterogeneities within the Earth splits the modes and lifts this degeneracy. The occurrence of the Great Sumatra-Andaman earthquake on 24 December 2004 provided unprecedented high-quality seismic data recorded by the broadband stations of the FDSN (Federation of Digital Seismograph Networks). For the first time, it has been possible to observe a very large collection of split modes, not only spheroidal modes but also toroidal modes.
Christian Corda
2015-01-01
Full Text Available Some recent important results on black hole (BH quantum physics concerning the BH effective state and the natural correspondence between Hawking radiation and BH quasi-normal modes (QNMs are reviewed, clarified, and refined. Such a correspondence permits one to naturally interpret QNMs as quantum levels in a semiclassical model. This is a model of BH somewhat similar to the historical semiclassical model of the structure of a hydrogen atom introduced by Bohr in 1913. In a certain sense, QNMs represent the “electron” which jumps from a level to another one and the absolute values of the QNMs frequencies, “triggered” by emissions (Hawking radiation and absorption of particles, represent the energy “shells” of the “gravitational hydrogen atom.” Important consequences on the BH information puzzle are discussed. In fact, it is shown that the time evolution of this “Bohr-like BH model” obeys a time dependent Schrödinger equation which permits the final BH state to be a pure quantum state instead of a mixed one. Thus, information comes out in BH evaporation in agreement with the assumption by ’t Hooft that Schröedinger equations can be used universally for all dynamics in the universe. We also show that, in addition, our approach solves the entanglement problem connected with the information paradox.
Some recent important results on black hole (BH) quantum physics concerning the BH effective state and the natural correspondence between Hawking radiation and BH quasi-normal modes (QNMs) are reviewed, clarified, and refined. Such a correspondence permits one to naturally interpret QNMs as quantum levels in a semiclassical model. This is a model of BH somewhat similar to the historical semiclassical model of the structure of a hydrogen atom introduced by Bohr in 1913. In a certain sense, QNMs represent the “electron” which jumps from a level to another one and the absolute values of the QNMs frequencies, “triggered” by emissions (Hawking radiation) and absorption of particles, represent the energy “shells” of the “gravitational hydrogen atom.” Important consequences on the BH information puzzle are discussed. In fact, it is shown that the time evolution of this “Bohr-like BH model” obeys a time dependent Schrödinger equation which permits the final BH state to be a pure quantum state instead of a mixed one. Thus, information comes out in BH evaporation in agreement with the assumption by ’t Hooft that Schröedinger equations can be used universally for all dynamics in the universe. We also show that, in addition, our approach solves the entanglement problem connected with the information paradox
罗虹; 章竟成; 李兴泉; 李英强
2013-01-01
A method to cutoff substructure low order normal modes in component mode synthesis is proposed. Frequency shifting technique is introduced in substructure free vibration differential equation. Quasi-static constraint mode is taken into coordinate transformation and the contribution of substructure low order normal modes to system middle frequency modes is reduced,thus substructure low order normal modes truncation is achieved. This technique is used to compute dynamic characteristics of a body-in-white FEM mode in the frequency band of 160 ～ 190 Hz. The results show that compared with traditional component mode synthesis,which keeps 1 836 normal modes,this method only needs 297 normal modes and saves 27. 7% calculation time. It means frequency shifting technique can improve the computational efficiency for middle frequency band dynamic characteristics of complex structure.%提出固定界面模态综合法中子结构低阶主模态的截断方法.对子结构自由振动微分方程做移频处理,采用包含惯性力影响因素的子结构准静力模态进行坐标变换,降低了子结构低阶主模态对系统中频段模态的贡献,实现了子结构低阶主模态截断.采用该方法分析某白车身有限元模型160～190 Hz的动态响应特性.结果表明:引入移频技术后,相比传统固定界面模态综合法,子结构保留的主模态数量从之前的1 836阶下降至297阶,计算时间减少27.7％,说明该方法能有效提高复杂结构中频段动态响应计算效率.
Hu, Xiao Gang
2016-08-01
Normal mode coupling pair 0S26-0T26 and 0S27-0T27 are significantly present at the South Pole station QSPA after the 2011/03/11 Mw9.1 Tohoku earthquake. In an attempt to determine the mechanisms responsible for the coupling pairs, I first investigate mode observations at 43 stations distributed along the polar great-circle path for the earthquake and observations at 32 Antarctic stations. I rule out the effect of Earth's rotation as well as the effect of global large-scale lateral heterogeneity, but argue instead for the effect of small-scale local azimuthal anisotropy in a depth extent about 300 km. The presence of quasi-Love waveform in 2-5 mHz at QSPA and its nearby stations confirms the predication. Secondly, I analyze normal mode observations at the South Pole location after 28 large earthquakes from 1998 to 2015. The result indicates that the presence of the mode coupling is azimuthal dependent, which is related to event azimuths in -46° to -18°. I also make a comparison between the shear-wave splitting measurements of previous studies and the mode coupling observations of this study, suggesting that their difference can be explained by a case that the anisotropy responsible for the mode coupling is not just below the South Pole location but located below region close to the Transantarctic Mountains (TAM). Furthermore, more signals of local azimuthal anisotropy in normal-mode observations at QSPA and SBA, such as coupling of 0S12-0T11 and vertical polarization anomaly for 0T10, confirms the existence of deep anisotropy close to TAM, which may be caused by asthenospheric mantle flow and edge convection around cratonic keel of TAM.
Arindam Chakraborty
2006-03-01
Full Text Available In order to settle the issue of equivalence or non-equivalence of the two lone pairsof electrons on oxygen atom in water molecule, a quantum chemical study of the dipolecorrelation of the electronic structure of the molecule as a function of conformationsgenerated following the normal modes of vibrations between the two extremeconformations, C2v (Ã¢ÂˆÂ HOH at 90o and DÃ¢ÂˆÂh (Ã¢ÂˆÂ HOH at 180o, including the equilibrium one,has been performed. The study invokes quantum mechanical partitioning of moleculardipoles into bond moment and lone pair moment and localization of delocalized canonicalmolecular orbitals, CMOÃ¢Â€Â™s into localized molecular orbitals, LMOÃ¢Â€Â™s. An earlier suggestion,on the basis of photoelectron spectroscopy, that one lone pair is in p-type and the other is ins-type orbital of O atom of water molecule at its equilibrium shape, and also the qualitativeÃ¢Â€ÂœSquirrel EarsÃ¢Â€Â structure are brought under serious scrutiny. A large number ofconformations are generated and the charge density matrix, dipole moment of eachconformation is computed in terms of the generated canonical molecular orbitals, CMOÃ¢Â€Â™sand then SinanoÃ„ÂŸluÃ¢Â€Â™s localization method is invoked to localize the CMOÃ¢Â€Â™s of eachconformation and the quantum mechanical hybridizations of all the bonds and lone pairs onO center are evaluated in terms of the localized molecular orbitals. Computed datademonstrate that the electronic structures i.e. two bond pairs and two lone pairs and itshybridization status of all conformations of water molecule are straightforward in terms ofthe LMOÃ¢Â€Â™s. It is further revealed that the pattern of orbital hybridization changescontinuously as a function of evolution of molecular shape. The close analysis of thegenerated LMOÃ¢Â€Â™s reveals that one lone pair is accommodated in a pure p orbital and anotherlone pair is in a hybrid
Refringence, field theory and normal modes
In a previous paper [Barcelo C et al 2001 Class. Quantum Grav. 18 3595-610 (Preprint gr-qc/0104001)] we have shown that the occurrence of curved spacetime 'effective Lorentzian geometries' is a generic result of linearizing an arbitrary classical field theory around some nontrivial background configuration. This observation explains the ubiquitous nature of the 'analogue models' for general relativity that have recently been developed based on condensed matter physics. In the simple (single scalar field) situation analysed in our previous paper, there is a single unique effective metric; more complicated situations can lead to bi-metric and multi-metric theories. In the present paper we will investigate the conditions required to keep the situation under control and compatible with experiment - either by enforcing a unique effective metric (as would be required to be strictly compatible with the Einstein equivalence principle), or at the worst by arranging things so that there are multiple metrics that are all 'close' to each other (in order to be compatible with the Eoetvoes experiment). The algebraically most general situation leads to a physical model whose mathematical description requires an extension of the usual notion of Finsler geometry to a Lorentzian-signature pseudo-Finsler geometry; while this is possibly of some interest in its own right, this particular case does not seem to be immediately relevant for either particle physics or gravitation. The key result is that wide classes of theories lend themselves to an effective metric description. This observation provides further evidence that the notion of 'analogue gravity' is rather generic
Normal mode calculations of trigonal selenium
Hansen, Flemming Yssing; McMurry, H. L.
1980-01-01
The phonon dispersion relations for trigonal selenium have been calculated on the basis of a short range potential field model. Electrostatic long range forces have not been included. The force field is defined in terms of symmetrized coordinates which reflect partly the symmetry of the space group...
Analog gravity from field theory normal modes?
Barcelo, Carlos; Liberati, Stefano; Visser, Matt
2001-01-01
We demonstrate that the emergence of a curved spacetime ``effective Lorentzian geometry'' is a common and generic result of linearizing a field theory around some non-trivial background. This investigation is motivated by considering the large number of ``analog models'' of general relativity that have recently been developed based on condensed matter physics, and asking whether there is something more fundamental going on. Indeed, linearization of a classical field theory (a field theoretic ...
Oda, Hitoshi
2016-06-01
The aspherical structure of the Earth is described in terms of lateral heterogeneity and anisotropy of the P- and S-wave velocities, density heterogeneity, ellipticity and rotation of the Earth and undulation of the discontinuity interfaces of the seismic wave velocities. Its structure significantly influences the normal mode spectra of the Earth's free oscillation in the form of cross-coupling between toroidal and spheroidal multiplets and self-coupling between the singlets forming them. Thus, the aspherical structure must be conversely estimated from the free oscillation spectra influenced by the cross-coupling and self-coupling. In the present study, we improve a spectral fitting inversion algorithm which was developed in a previous study to retrieve the global structures of the isotropic and anisotropic velocities of the P and S waves from the free oscillation spectra. The main improvement is that the geographical distribution of the intensity of the S-wave azimuthal anisotropy is represented by a nonlinear combination of structure coefficients for the anisotropic velocity structure, whereas in the previous study it was expanded into a generalized spherical harmonic series. Consequently, the improved inversion algorithm reduces the number of unknown parameters that must be determined compared to the previous inversion algorithm and employs a one-step inversion method by which the structure coefficients for the isotropic and anisotropic velocities are directly estimated from the fee oscillation spectra. The applicability of the improved inversion is examined by several numerical experiments using synthetic spectral data, which are produced by supposing a variety of isotropic and anisotropic velocity structures, earthquake source parameters and station-event pairs. Furthermore, the robustness of the inversion algorithm is investigated with respect to the back-ground noise contaminating the spectral data as well as truncating the series expansions by finite terms
Zürn, W.; Ferreira, A. M. G.; Widmer-Schnidrig, R.; Lentas, K.; Rivera, L.; Clévédé, E.
2015-12-01
We present spectra concentrating on the lowest-frequency normal modes of the Earth obtained from records of the invar-wire strainmeters and STS-1 broad-band seismometers located in the Black Forest Observatory, Germany after the disastrous earthquakes off the NW coast of Sumatra in 2004 and off the coast near Tohoku, Japan in 2011. We compare the spectra to ones obtained from synthetic seismograms computed using a mode summation technique for an anelastic, elliptical, rotating, spherically symmetric Earth model. The synthetics include strain-strain-coupling effects by using coupling coefficients obtained from comparisons between Earth tide signals recorded by the strainmeters and synthetic tidal records. We show that for the low-frequency toroidal and spheroidal modes up to 1 mHz, the strainmeters produce better signal-to-noise ratios than the broad-band horizontal seismometers. Overall, the comparison with the synthetics is satisfactory but not as good as for vertical accelerations. In particular, we demonstrate the high quality of the strainmeter data by showing the Coriolis splitting of toroidal modes for the first time in individual records, the first clear observation of the singlet _2S_1^0 and the detection of the fundamental radial mode 0S0 with good signal-to-noise ratio and with a strain amplitude of 10-11. We also identify the latter mode in a record of the Isabella strainmeter after the great Chilean quake in 1960, the detection of which was missed by the original studies.
A quantitative analysis of coupled oscillations using mobile accelerometer sensors
Castro-Palacio, Juan Carlos; Velázquez-Abad, Luisberis; Giménez, Fernando; Monsoriu, Juan A.
2013-05-01
In this paper, smartphone acceleration sensors were used to perform a quantitative analysis of mechanical coupled oscillations. Symmetric and asymmetric normal modes were studied separately in the first two experiments. In the third, a coupled oscillation was studied as a combination of the normal modes. Results indicate that acceleration sensors of smartphones, which are very familiar to students, represent valuable measurement instruments for introductory and first-year physics courses.
A quantitative analysis of coupled oscillations using mobile accelerometer sensors
In this paper, smartphone acceleration sensors were used to perform a quantitative analysis of mechanical coupled oscillations. Symmetric and asymmetric normal modes were studied separately in the first two experiments. In the third, a coupled oscillation was studied as a combination of the normal modes. Results indicate that acceleration sensors of smartphones, which are very familiar to students, represent valuable measurement instruments for introductory and first-year physics courses. (paper)
Evaluation of MARC for the analysis of rotating composite blades
Bartos, Karen F.; Ernst, Michael A.
1993-01-01
The suitability of the MARC code for the analysis of rotating composite blades was evaluated using a four-task process. A nonlinear displacement analysis and subsequent eigenvalue analysis were performed on a rotating spring mass system to ensure that displacement-dependent centrifugal forces were accounted for in the eigenvalue analysis. Normal modes analyses were conducted on isotropic plates with various degrees of twist to evaluate MARC's ability to handle blade twist. Normal modes analyses were conducted on flat composite plates to validate the newly developed coupled COBSTRAN-MARC methodology. Finally, normal modes analyses were conducted on four composite propfan blades that were designed, analyzed, and fabricated at NASA Lewis Research Center. Results were compared with experimental data. The research documented herein presents MARC as a viable tool for the analysis of rotating composite blades.
Electromagnetic fluctuations and normal modes of a drifting relativistic plasma
Ruyer, C; Bénisti, D; Bonnaud, G
2013-01-01
We present an exact calculation of the power spectrum of the electromagnetic fluctuations in a relativistic equilibrium plasma described by Maxwell-J\\"uttner distribution functions. We consider the cases of wave vectors parallel or normal to the plasma mean velocity. The relative contributions of the subluminal and supraluminal fluctuations are evaluated. Analytical expressions of the spatial fluctuation spectra are derived in each case. These theoretical results are compared to particle-in-cell simulations, showing a good reproduction of the subluminal fluctuation spectra.
Hydra Hammer Manifold and MDC tip characterization (normal mode)
Dynamic tests were performed on prototype designs of manifold and mild detonating cord (MDC) components for the Hydra Hammer Disablement System. MDC end tips and manifold formed flyers, axial and radial, were photograhically covered to determine flyer shapes, velocities, and transit times
The normal modes of lattice vibrations of ice XI
Zhang, Peng; Wang, Zhe; Lu, Ying-Bo; Ding, Zheng-Wen
2016-07-01
The vibrational spectrum of ice XI at thermal wavelengths using the CASTEP code, a first-principles simulation method, is investigated. A dual-track approach is constructed to verify the validity for the computational phonon spectrum: collate the simulated spectrum with inelastic neutron scattering experiments and assign the photon scattering peaks according to the calculated normal vibration frequencies. The 33 optical normal vibrations at the Brillouin center are illustrated definitely from the ab initio outcomes. The depolarizing field effect of the hydrogen bond vibrations at frequencies of 229 cm‑1 and 310 cm‑1 is found to agree well with the LST relationship. It is a convincing evidence to manifest the LO-TO splitting of hydrogen bonds in ice crystal. We attribute the two hydrogen bond peaks to the depolarization effect and apply this viewpoint to ordinary ice phase, ice Ih, which is difficult to analyse their vibration modes due to proton disorder.
Dynamical analysis of highly excited molecular spectra
Kellman, M.E. [Univ. of Oregon, Eugene (United States)
1993-12-01
The goal of this program is new methods for analysis of spectra and dynamics of highly excited vibrational states of molecules. In these systems, strong mode coupling and anharmonicity give rise to complicated classical dynamics, and make the simple normal modes analysis unsatisfactory. New methods of spectral analysis, pattern recognition, and assignment are sought using techniques of nonlinear dynamics including bifurcation theory, phase space classification, and quantization of phase space structures. The emphasis is chaotic systems and systems with many degrees of freedom.
Analysis of nonlinear structures via mode synthesis
Gieseke, R. K.
1975-01-01
An effective procedure for NASTRAN was developed that permits any number of substructures of any size to be synthesized for the purpose of developing normal modes of vibration of the complete structural system. The technique is extended to permit modal transient analysis of the subdivided system. This latter procedure permits the use of NASTRAN's ability to include nonlinear forces in the problem. The five-phase process is accomplished using standard NASTRAN rigid formats with problem-independent alter packages and DMAP sequences.
Green's-function analysis of the odd-parity perturbations of a Reissner-Nordstroem black hole
Chitre, D.M.; Chrzanowski, P.L.
1976-11-15
A Green's-function analysis is carried out for Reissner-Nordstroem odd-parity perturbation equations with sources. It leads to a definitive identification of the normal modes, which are shown to contain a derivative coupling of the gravitational and electromagnetic potentials to the background electromagnetic field. Connections are made with previous works by Gerlach in the high-frequency limit and by Chitre, Price, and Sandberg in the small-charge approximation. (AIP)
Zeitler, Todd R.; Greathouse, Jeffery A.; Gale, Julian D.; Cygan, Randall T.
2014-01-01
We introduce a nonbonded three-body harmonic potential energy term for Mg–O–H interactions for improved edge surface stability in molecular simulations. The new potential term is compatible with the Clayff force field and is applied here to brucite, a layered magnesium hydroxide mineral. Comparisons of normal mode frequencies from classical and density functional theory calculations are used to verify a suitable spring constant (k parameter) for the Mg–O–H bending motion. Vibrational analysis...
Wang, Qi; Pang, Yuan-Ping
2007-01-01
The energy minimization of a small molecule alone does not automatically stop at a local minimum of the potential energy surface of the molecule if the minimum is shallow, thus leading to folding of the molecule and consequently hampering the generation of the bound conformation of a guest in the absence of its host. This questions the practicality of virtual screening methods that use conformations at local minima of their potential energy surfaces (local minimum conformations) as potential ...
Normal modes and vortex dynamics in 2D easy-axis ferromagnets
Magnon modes, localized on vortices in easy-axis 2-D ferromagnets are studied. There are local modes for all values of quantum numbers m in a definite frequency range, determined by the strength of anisotropy. Connected with the translational mode, the vortex dynamics problem is considered. The momentum of individual moving vortex is calculated based on the exact solution of equations for vortex motion in the isotropic case. The momentum balance equation with the Magnus-type force for the systems of vortices is derived. (author). 11 refs
The detection of Jupiter normal modes with gravity measurements of the mission Juno
Durante, D.; Iess, L.
2015-10-01
Arriving at Jupiter on July 4, 2016, NASA's Juno mission will complete 37 orbits (14-days period) around the planet, revealing details of the interior structure and composition, a crucial aspect to understand the origin and evolution of Jupiter. A radio science experiment will help to select and validate the existing models of Jupiter internal composition, in particular the mass of the silicate core.
Bernard, Simon; Marrelec, Guillaume; Laugier, Pascal; Grimal, Quentin
2015-06-01
Resonant ultrasound spectroscopy is an experimental technique for measuring the stiffness of anisotropic solid materials. The free vibration resonant frequencies of a specimen are measured and the stiffness coefficients of the material adjusted to minimize the difference between experimental and predicted frequencies. An issue of this inverse approach is that the measured frequencies are not easily paired with their predicted counterpart, leading to ambiguities in the definition of the objective function. In the past, this issue has been overcome through trial-and-error methods requiring the experimentalist to find the correct pairing, or through involved experimental methods measuring the shapes of the normal vibration modes in addition to their frequencies. The purpose of this work is to show, through a Bayesian formulation, that the inverse problem can be solved automatically and without requiring additions to the usual experimental setup. The pairing of measured and predicted frequencies is considered unknown, and the joint posterior probability distribution of pairing and stiffness is sampled using Markov chain Monte Carlo. The method is illustrated on two published data sets. The first set includes the exact pairing, allowing validation of the method. The second application deals with attenuative materials, for which many predicted modes cannot be observed, further complicating the inverse problem. In that case, introduction of prior information through Bayesian formulation reduces ambiguities.
Stable, accurate and efficient computation of normal modes for horizontal stratified models
Wu, Bo; Chen, Xiaofei
2016-08-01
We propose an adaptive root-determining strategy that is very useful when dealing with trapped modes or Stoneley modes whose energies become very insignificant on the free surface in the presence of low-velocity layers or fluid layers in the model. Loss of modes in these cases or inaccuracy in the calculation of these modes may then be easily avoided. Built upon the generalized reflection/transmission coefficients, the concept of `family of secular functions' that we herein call `adaptive mode observers' is thus naturally introduced to implement this strategy, the underlying idea of which has been distinctly noted for the first time and may be generalized to other applications such as free oscillations or applied to other methods in use when these cases are encountered. Additionally, we have made further improvements upon the generalized reflection/transmission coefficient method; mode observers associated with only the free surface and low-velocity layers (and the fluid/solid interface if the model contains fluid layers) are adequate to guarantee no loss and high precision at the same time of any physically existent modes without excessive calculations. Finally, the conventional definition of the fundamental mode is reconsidered, which is entailed in the cases under study. Some computational aspects are remarked on. With the additional help afforded by our superior root-searching scheme and the possibility of speeding calculation using a less number of layers aided by the concept of `turning point', our algorithm is remarkably efficient as well as stable and accurate and can be used as a powerful tool for widely related applications.
High-average-power normal-mode Cr:Nd:GSGG lasers
Several recent studies have shown the laser host material gadolinium scandium gallium garnet (GSGG) doped with Nd/sup 3+/ and sensitized by Cr/sup 3+/ to be a more efficient laser than the well-known commonly used Nd:YAG. However, all these studies have been performed at relatively low average pump power. To evaluate Nd:GSGG as a high-average-power laser material, the authors measured absorption efficiency, heat deposition rate, and thermally induced stress in 4- and 6.3-mm diam GSGG laser rods up to 2-KW pumping levels and compared these values, as well as laser output powers, to the results of similar experiments in Nd:YAG. In this work, 79-mm long Cr:Nd:GSGG rods have been tested using a silver-plated elliptical pump reflector which housed a xenon flashlamp running at a 6-Hz repetition rate with a pulse duration of ≅500 μs. The authors used the frequency-doubled output from a cw Nd:YAG laser at 532 nm as a probe beam to measure average thermal focal length and thermally induced birefringence
Bisymmetric normal modes in soft-centred and realistic galactic discs
Polyachenko, Evgeny
2014-01-01
We test methods for the determination of unstable modes in stellar discs: a point collocation scheme in the action sub-space, a scheme based on expansion of the density and potential on the biorthonormal basis, and a finite element method. Using models of galaxies with low and high mass concentration to the center, the existence of two different kinds of spectra of unstable modes is demonstrated. Characteristic features of methods and obtained spectra are discussed. Despite ignoring any constraint on the continuity or differentiability of the perturbed DF, the collocation scheme is reliable for obtaining spectra and patterns in both kinds of models. The method based on the expansion of the perturbed potential and surface density over a biorthogonal basis was not applicable to a model with high mass concentration. The finite element method successfully used in various fields of science and engineering is currently sensitive to the presence of resonant orbits due to the choice of interpolation functions for the...
On the structure and normal modes of hydrogenated Ti-fullerene compounds
Tlahuice-Flores, Alfredo, E-mail: tlahuicef@yahoo.com [Universidad Nacional Autonoma de Mexico, Instituto de Fisica (Mexico); Mejia-Rosales, Sergio, E-mail: sergio.mejiars@uanl.edu.mx [Universidad Autonoma de Nuevo Leon, CICFIM-Facultad de Ciencias Fisico Matematicas, and Centro de Innovacion, Investigacion y Desarrollo en Ingenieria y Tecnologia (Mexico); Galvan, Donald H., E-mail: donald@cnyn.unam.mx [Centro de Nanociencias y Nanotecnologia-Universidad Nacional Autonoma de Mexico (Mexico)
2012-08-15
When titanium covers a C{sub 60} core, the metal atoms may suppress the fullerene's capacity of storing hydrogen, depending on the number of Ti atoms covering the C{sub 60} framework, the Ti-C binding energy, and diffusion barriers. In this article, we study the structural and vibrational properties of the C{sub 60}TiH{sub n} (n = 2, 4, 6, and 8) and C{sub 60}Ti{sub 6}H{sub 48} compounds. The IR spectra of C{sub 60}TiH{sub n} compounds have a maximum attributable to the Ti-H stretching mode, which shifts to lower values in the structures with n = 4, 8, while their Raman spectra show two peaks corresponding to the stretching modes of H{sub 2} molecules at apical and azimuthal positions. On the other hand, the IR spectrum of C{sub 60}Ti{sub 6}H{sub 48} shows an intense peak due to the Ti-H in-phase stretching mode, while its Raman spectrum has a maximum attributed to the pentagonal pinch of the C{sub 60} core. Finally, we have found that the presence of one apical H{sub 2} molecule enhances the pentagonal pinch mode, becoming the maximum in the Raman spectrum.Graphical Abstract.
Rueda, Manuel; Bottegoni, Giovanni; Abagyan, Ruben
2009-01-01
The representation of protein flexibility is still a challenge for the state-of-the-art flexible ligand docking protocols. In this article we use a large and diverse benchmark to prove that is possible to improve consistently the cross docking performance against a single receptor conformation by using an equilibrium ensemble of binding site conformers. The benchmark contained 28 proteins, and the top ranked near native poses for the ligand were found 20% more efficiently than using a single ...
Automated Analysis, Classification, and Display of Waveforms
Kwan, Chiman; Xu, Roger; Mayhew, David; Zhang, Frank; Zide, Alan; Bonggren, Jeff
2004-01-01
A computer program partly automates the analysis, classification, and display of waveforms represented by digital samples. In the original application for which the program was developed, the raw waveform data to be analyzed by the program are acquired from space-shuttle auxiliary power units (APUs) at a sampling rate of 100 Hz. The program could also be modified for application to other waveforms -- for example, electrocardiograms. The program begins by performing principal-component analysis (PCA) of 50 normal-mode APU waveforms. Each waveform is segmented. A covariance matrix is formed by use of the segmented waveforms. Three eigenvectors corresponding to three principal components are calculated. To generate features, each waveform is then projected onto the eigenvectors. These features are displayed on a three-dimensional diagram, facilitating the visualization of the trend of APU operations.
Fully-Coupled Fluid/Structure Vibration Analysis Using MSC/NASTRAN
Fernholz, Christian M.; Robinson, Jay H.
1996-01-01
MSC/NASTRAN's performance in the solution of fully-coupled fluid/structure problems is evaluated. NASTRAN is used to perform normal modes (SOL 103) and forced-response analyses (SOL 108, 111) on cylindrical and cubic fluid/structure models. Bulk data file cards unique to the specification of a fluid element are discussed and analytic partially-coupled solutions are derived for each type of problem. These solutions are used to evaluate NASTRAN's solutions for accuracy. Appendices to this work include NASTRAN data presented in fringe plot form, FORTRAN source code listings written in support of this work, and NASTRAN data file usage requirements for each analysis.
TMM@: a web application for the analysis of transmembrane helix mobility
Jonassen Inge
2007-07-01
Full Text Available Abstract Background To understand the mechanism by which a protein transmits a signal through the cell membrane, an understanding of the flexibility of its transmembrane (TM region is essential. Normal Mode Analysis (NMA has become the method of choice to investigate the slowest motions in macromolecular systems. It has been widely used to study transmembrane channels and pumps. It relies on the hypothesis that the vibrational normal modes having the lowest frequencies (also named soft modes describe the largest movements in a protein and are the ones that are functionally relevant. In particular NMA can be used to study dynamics of TM regions, but no tool making this approach available for non-experts, has been available so far. Results We developed the web-application TMM@ (TransMembrane α-helical Mobility analyzer. It uses NMA to characterize the propensity of transmembrane α-helices to be displaced. Starting from a structure file at the PDB format, the server computes the normal modes of the protein and identifies which helices in the bundle are the most mobile. Each analysis is performed independently from the others and results can be visualized using only a web browser. No additional plug-in or software is required. For users who would like to further analyze the output data with their favourite software, raw results can also be downloaded. Conclusion We built a novel and unique tool, TMM@, to study the mobility of transmembrane α-helices. The tool can be applied to for example membrane transporters and provides biologists studying transmembrane proteins with an approach to investigate which α-helices are likely to undergo the largest displacements, and hence which helices are most likely to be involved in the transportation of molecules in and out of the cell.
Krüger, Sascha; Grotemeyer, Jürgen
2016-03-14
Resonance enhanced multiphoton ionization (REMPI) and mass analyzed threshold ionization (MATI) spectroscopy have been applied in order to investigate the vibrational structure of 1,2-dichloro-4-fluorobenzene (1,2,4-DCFB) in its first excited state (S1) and the cationic ground state (D0). The selection of the state prior to ionization resulted in MATI spectra with different intensity distributions thus giving access to many vibrational levels. To support the experimental findings, geometry optimizations and frequency analyses at DFT (density functional) and TDDFT (time-dependent density functional) levels of theory have been applied. Additionally, a multidimensional Franck-Condon approach has been used to calculate the vibrational intensities from the DFT calculations. An excellent agreement between simulated and measured REMPI and MATI spectra allowed for a confident assignment of vibrational levels and mechanisms active during excitation and ionization. In order to avoid any ambiguity regarding the assignment of the vibrational bands to normal modes, Duschinsky normal mode analysis has been performed to correlate the ground state (S0) normal modes of 1,2,4-DCFB with the benzene derived Wilson nomenclature. From the REMPI spectra the electronic excitation energy (EE) of 1,2-dichloro-4-fluorobenzene could be determined to be 35 714 ± 2 cm(-1) while the MATI spectra yielded the adiabatic ionization energy (IE) of 1,2-dichloro-4-fluorobenzene which could be determined to be 73 332 ± 7 cm(-1). PMID:26884269
Normal vibrational frequencies and absolute IR band intensities of the biologically active steroid phytohormones homobrassinolide and (22S,23S)-homobrassinolide were calculated in the framework of an original approach that combined classical analysis of normal modes using molecular mechanics with quantum-chemical estimation of the absolute intensities. IR absorption bands were interpreted based on a comparison of the experimental and theoretical absorption spectra. The impact of structural differences in the side chains of these molecules on the formation of their IR spectra in the region 1500-950 cm -1 was estimated. (authors)
Andrianov, V. M.; Korolevich, M. V.
2015-09-01
Normal vibrational frequencies and absolute IR band intensities of the biologically active steroid phytohormones homobrassinolide and (22S,23S)-homobrassinolide were calculated in the framework of an original approach that combined classical analysis of normal modes using molecular mechanics with quantum-chemical estimation of the absolute intensities. IR absorption bands were interpreted based on a comparison of the experimental and theoretical absorption spectra. The impact of structural differences in the side chains of these molecules on the formation of their IR spectra in the region 1500-950 cm -1 was estimated.
Structure network analysis to gain insights into GPCR function.
Fanelli, Francesca; Felline, Angelo; Raimondi, Francesco; Seeber, Michele
2016-04-15
G protein coupled receptors (GPCRs) are allosteric proteins whose functioning fundamentals are the communication between the two poles of the helix bundle. Protein structure network (PSN) analysis is one of the graph theory-based approaches currently used to investigate the structural communication in biomolecular systems. Information on system's dynamics can be provided by atomistic molecular dynamics (MD) simulations or coarse grained elastic network models paired with normal mode analysis (ENM-NMA). The present review article describes the application of PSN analysis to uncover the structural communication in G protein coupled receptors (GPCRs). Strategies to highlight changes in structural communication upon misfolding, dimerization and activation are described. Focus is put on the ENM-NMA-based strategy applied to the crystallographic structures of rhodopsin in its inactive (dark) and signalling active (meta II (MII)) states, highlighting changes in structure network and centrality of the retinal chromophore in differentiating the inactive and active states of the receptor. PMID:27068978
An Aeroelastic Analysis of a Thin Flexible Membrane
Scott, Robert C.; Bartels, Robert E.; Kandil, Osama A.
2007-01-01
Studies have shown that significant vehicle mass and cost savings are possible with the use of ballutes for aero-capture. Through NASA's In-Space Propulsion program, a preliminary examination of ballute sensitivity to geometry and Reynolds number was conducted, and a single-pass coupling between an aero code and a finite element solver was used to assess the static aeroelastic effects. There remain, however, a variety of open questions regarding the dynamic aeroelastic stability of membrane structures for aero-capture, with the primary challenge being the prediction of the membrane flutter onset. The purpose of this paper is to describe and begin addressing these issues. The paper includes a review of the literature associated with the structural analysis of membranes and membrane utter. Flow/structure analysis coupling and hypersonic flow solver options are also discussed. An approach is proposed for tackling this problem that starts with a relatively simple geometry and develops and evaluates analysis methods and procedures. This preliminary study considers a computationally manageable 2-dimensional problem. The membrane structural models used in the paper include a nonlinear finite-difference model for static and dynamic analysis and a NASTRAN finite element membrane model for nonlinear static and linear normal modes analysis. Both structural models are coupled with a structured compressible flow solver for static aeroelastic analysis. For dynamic aeroelastic analyses, the NASTRAN normal modes are used in the structured compressible flow solver and 3rd order piston theories were used with the finite difference membrane model to simulate utter onset. Results from the various static and dynamic aeroelastic analyses are compared.
Ghysels, A.; Van Neck, D.; Waroquier, M.
2007-10-01
Partial optimization is a useful technique to reduce the computational load in simulations of extended systems. In such nonequilibrium structures, the accurate calculation of localized vibrational modes can be troublesome, since the standard normal mode analysis becomes inappropriate. In a previous paper [A. Ghysels et al., J. Chem. Phys. 126, 224102 (2007)], the mobile block Hessian (MBH) approach was presented to deal with the vibrational analysis in partially optimized systems. In the MBH model, the nonoptimized regions of the system are represented by one or several blocks, which can move as rigid bodies with respect to the atoms of the optimized region. In this way unphysical imaginary frequencies are avoided and the translational/rotational invariance of the potential energy surface is fully respected. In this paper we focus on issues concerning the practical numerical implementation of the MBH model. The MBH normal mode equations are worked out for several coordinate choices. The introduction of a consistent group-theoretical notation facilitates the treatment of both the case of a single block and the case of multiple blocks. Special attention is paid to the formulation in terms of Cartesian variables, in order to provide a link with the standard output of common molecular modeling programs.
Araki, Keisuke
2015-12-01
The dynamics of an incompressible, dissipationless Hall magnetohydrodynamic medium are investigated from Lagrangian mechanical viewpoint. The hybrid and magnetic helicities are shown to emerge, respectively, from the application of the particle relabeling symmetry for ion and electron flows to Noether's first theorem, while the constant of motion associated with the theorem is generally given by their arbitrary linear combination. Furthermore, integral path variation associated with the invariant action is expressed by the operation of an integrodifferential operator on the reference path. The eigenfunctions of this operator are double Beltrami flows, i.e., force-free stationary solutions to the equation of motion and provide a family of orthogonal function bases that yields the spectral representation of the equation of motion with a remarkably simple form. Among the double Beltrami flows, considering the influence of a uniform background magnetic field and the Hall term effect vanishing limit, the generalized Elsässer variables are found to be the most suitable for avoiding problems with singularities in the standard magnetohydrodynamic limit. PMID:26764837
Merchant, D. H.; Gates, R. M.; Straayer, J. W.
1975-01-01
The effect of localized structural damping on the excitability of higher-order large space telescope spacecraft modes is investigated. A preprocessor computer program is developed to incorporate Voigt structural joint damping models in a finite-element dynamic model. A postprocessor computer program is developed to select critical modes for low-frequency attitude control problems and for higher-frequency fine-stabilization problems. The selection is accomplished by ranking the flexible modes based on coefficients for rate gyro, position gyro, and optical sensor, and on image-plane motions due to sinusoidal or random PSD force and torque inputs.
Comandi, G L; Chiofalo, M L; Nobili, A M; Polacco, E; Toncelli, R
2006-01-01
Recent theoretical work suggests that violation of the Equivalence Principle might be revealed in a measurement of the fractional differential acceleration $\\eta$ between two test bodies -of different composition, falling in the gravitational field of a source mass- if the measurement is made to the level of $\\eta\\simeq 10^{-13}$ or better. This being within the reach of ground based experiments, gives them a new impetus. However, while slowly rotating torsion balances in ground laboratories are close to reaching this level, only an experiment performed in low orbit around the Earth is likely to provide a much better accuracy. We report on the progress made with the "Galileo Galilei on the Ground" (GGG) experiment, which aims to compete with torsion balances using an instrument design also capable of being converted into a much higher sensitivity space test. In the present and following paper (Part I and Part II), we demonstrate that the dynamical response of the GGG differential accelerometer set into superc...
Ren, Yinghui; Li, Bin; Bian, Wensheng
2011-02-14
Full-dimensional quantum dynamics calculations of vinylidene-acetylene isomerization are performed and the state-specific resonance decay lifetimes of vinylidene(-d(2)) are computed. The theoretical scheme is a combination of several methods: normal coordinates are chosen to describe the nuclear motion of vinylidene, with both the parity and permutation symmetry exploited; phase space optimization in combination with physical considerations is used to generate an efficient discrete variable representation; the reaction coordinate is defined by us according to the three most relevant normal coordinates, along which a kind of optimal complex absorbing potential is imposed; the preconditioned inexact spectral transform method combined with an efficient preconditioner is employed to extract the energies and lifetimes of vinylidene. The overall computation is efficient. The computed energy levels generally agree with experiment well, and several state-specific lifetimes are reported for the first time. PMID:21186383
Anatomy of the binary black hole recoil: A multipolar analysis
Schnittman, Jeremy D; van Meter, James R; Baker, John G; Boggs, William D; Centrella, Joan; Kelly, Bernard J; McWilliams, Sean T
2007-01-01
We present a multipolar analysis of the gravitational recoil computed in recent numerical simulations of binary black hole (BH) coalescence, for both unequal masses and non-zero, non-precessing spins. We show that multipole moments up to and including l=4 are sufficient to accurately reproduce the final recoil velocity (within ~2%) and that only a few dominant modes contribute significantly to it (within ~5%). We describe how the relative amplitudes, and more importantly, the relative phases, of these few modes control the way in which the recoil builds up throughout the inspiral, merger, and ringdown phases. We also find that the numerical results can be reproduced by an ``effective Newtonian'' formula for the multipole moments obtained by replacing the radial separation in the Newtonian formulae with an effective radius computed from the numerical data. Beyond the merger, the numerical results are reproduced by a superposition of three Kerr quasi-normal modes (QNMs). Analytic formulae, obtained by expressin...
Flexibility Analysis of Bacillus thuringiensis Cry1Aa
ZHAO Xin Min; XIA Li Qiu; YANG Xiao Ping; PENG Xiao Yun
2015-01-01
Objective To investigate the flexibility and mobility of the Bacillus thuringiensis toxin Cry1Aa. Methods The graph theory-based program Constraint Network Analysis and normal mode-based program NMsim were used to analyze the global and local flexibility indices as well as the fluctuation of individual residues in detail. Results The decrease in Cry1Aa network rigidity with the increase of temperature was evident. Two phase transition points in which the Cry1Aa structure lost rigidity during the thermal simulation were identified. Two rigid clusters were found in domains I and II. Weak spots were found in C-terminal domain III. Several flexible regions were found in all three domains;the largest residue fluctuation was present in the apical loop2 of domain II. Conclusion Although several flexible regions could be found in all the three domains, the most flexible regions were in the apical loops of domain II.
Basic equations for large Larmor radius analysis of the electrostatic gravitation mode
The electrostatic flute-type instability in an inhomogeneous magnetic field is one of the most important modes in fusion research. A model of this mode in terms of an equivalent gravitation force has earlier been treated by conventional normal mode analysis, also including finite Larmor radius (FLR) effects. Such an analysis does not apply to the case of large particle excursions, such as those due to large Larmor radius (LLR) effects. At this stage there does not exist any analytic kinetic approach by which the LLR effects can be fully treated in a quasi-neutral plasma. The aim of this paper is not to present a final solution of the LLR effects on the present instability, but merely to formulate the basic equations for a proposed computer analysis. (author)
An eigenvalue analysis of finite-difference approximations for hyperbolic IBVPs
Warming, Robert F.; Beam, Richard M.
1990-01-01
The eigenvalue spectrum associated with a linear finite-difference approximation plays a crucial role in the stability analysis and in the actual computational performance of the discrete approximation. The eigenvalue spectrum associated with the Lax-Wendroff scheme applied to a model hyperbolic equation was investigated. For an initial-boundary-value problem (IBVP) on a finite domain, the eigenvalue or normal mode analysis is analytically intractable. A study of auxiliary problems (Dirichlet and quarter-plane) leads to asymptotic estimates of the eigenvalue spectrum and to an identification of individual modes as either benign or unstable. The asymptotic analysis establishes an intuitive as well as quantitative connection between the algebraic tests in the theory of Gustafsson, Kreiss, and Sundstrom and Lax-Richtmyer L (sub 2) stability on a finite domain.
Non-modal linear stability analysis of miscible viscous fingering in a Hele-Shaw cell
Hota, Tapan Kumar; Mishra, Manoranjan
2015-01-01
For miscible viscous fingering (VF) in a Hele-Shaw cell or in two dimensional homogeneous porous media, the transient growth of disturbances is investigated by non-modal linear stability analysis (NMA). Due to the non-autonomous nature of the linearized perturbed equations, the linear stability theory prohibits using the normal mode analysis. The linearized perturbed equations for Darcy's law coupled with a convection-diffusion equation is discretized using finite difference method. The resultant matrix valued initial value problem is then solved by fourth order Runge-Kutta method, followed by a singular value decomposition (SVD) of the propagator matrix. We demonstrate the dominant perturbation that experiences the maximum amplification within the linear regime which lead to the transient growth. This feature was previously unattained in the existing linear stability methods for miscible VF. To explore the relevance of the optimal perturbation obtained from non-modal analysis of the physical system, we perfo...
Fast dynamics perturbation analysis for prediction of protein functional sites
Cohn Judith D
2008-01-01
Full Text Available Abstract Background We present a fast version of the dynamics perturbation analysis (DPA algorithm to predict functional sites in protein structures. The original DPA algorithm finds regions in proteins where interactions cause a large change in the protein conformational distribution, as measured using the relative entropy Dx. Such regions are associated with functional sites. Results The Fast DPA algorithm, which accelerates DPA calculations, is motivated by an empirical observation that Dx in a normal-modes model is highly correlated with an entropic term that only depends on the eigenvalues of the normal modes. The eigenvalues are accurately estimated using first-order perturbation theory, resulting in a N-fold reduction in the overall computational requirements of the algorithm, where N is the number of residues in the protein. The performance of the original and Fast DPA algorithms was compared using protein structures from a standard small-molecule docking test set. For nominal implementations of each algorithm, top-ranked Fast DPA predictions overlapped the true binding site 94% of the time, compared to 87% of the time for original DPA. In addition, per-protein recall statistics (fraction of binding-site residues that are among predicted residues were slightly better for Fast DPA. On the other hand, per-protein precision statistics (fraction of predicted residues that are among binding-site residues were slightly better using original DPA. Overall, the performance of Fast DPA in predicting ligand-binding-site residues was comparable to that of the original DPA algorithm. Conclusion Compared to the original DPA algorithm, the decreased run time with comparable performance makes Fast DPA well-suited for implementation on a web server and for high-throughput analysis.
Maurin, Krzysztof
1980-01-01
The extraordinarily rapid advances made in mathematics since World War II have resulted in analysis becoming an enormous organism spread ing in all directions. Gone for good surely are the days of the great French "courses of analysis" which embodied the whole of the "ana lytical" knowledge of the times in three volumes-as the classical work of Camille Jordan. Perhaps that is why present-day textbooks of anal ysis are disproportionately modest relative to the present state of the art. More: they have "retreated" to the state before Jordan and Goursat. In recent years the scene has been changing rapidly: Jean Dieudon ne is offering us his monumentel Elements d'Analyse (10 volumes) written in the spirit of the great French Course d'Analyse. To the best of my knowledge, the present book is the only one of its size: starting from scratch-from rational numbers, to be precise-it goes on to the theory of distributions, direct integrals, analysis on com plex manifolds, Kahler manifolds, the theory of sheave...
NASTRAN component-mode synthesis
Guyan, R. J.
1976-01-01
Procedure for dynamic substructuring analysis technique is generally as follows: calculation of component modes; selection of component normal modes, calculation of component generalized matrices, assembly of system matrices, and computation of normal modes; and retrieval of component response.
R. Sekar
2013-05-01
Full Text Available Instability of themocovection in a multi-component fluid has wide range of applications in ionospheric, geothermal and industries. In this analysis, the effect of rotation and vertical anisotropy on Soret-driven thermoconvective instability in a ferrofluid has been studied. The fluid layer is assumed to be horizontal and is heated from below and salted from above. In momentum equation, the effect of both substantial derivatives and coriolis terms are considered. The resulting eigen value problem is solved using Brinkman model. A linear stability analysis is used for both stationary and oscillatory instabilities for different parameters for which normal mode technique is applied. The effect of rotation tends to stabilize the system and anisotropy and Soret effects tend to destabilize the system.
R. Sekar
2015-02-01
Full Text Available The Soret–driven ferro thermoconvective instability of multi–component fluid in a porous medium heated from below and salted from above in the presence of dust particles subjected to a transverse uniform magnetic field has been analyzed using Darcy model for various values of permeability of the porous medium. The salinity effect has been contained in magnetization and density of the ferrofluid. A small thermal perturbation imparted on the basic state and a linear stability analysis is used for this model for which normal mode technique is applied. An exact solution is obtained for the case of two free boundaries and both stationary and oscillatory instabilities have been investigated. It is found that the system destabilizes only through stationary mode. The non-buoyancy magnetization parameter, the dust particle parameter and the permeability of the porous medium are found to destabilize the system. The results are depicted graphically.
Singh, Ravindra Kumar; Singh, Ashok Kumar
2015-08-01
2-Acetylpyridine thiosemicarbazone was synthesized and characterized by elemental analysis, 1H, 13C NMR, IR, UV and ESI-MS mass spectrometry. Quantum chemical calculations have been performed at DFT level of theory using B3LYP functional and 6-31G (d, p) as basis set. Potential energy distribution (PED) for the normal modes of vibrations was done using Gar2ped program. The time dependent density functional theory (TD-DFT) was used to assign the various electronic transitions within molecule in gas as well as solvent phase. Non linear optical (NLO) behavior of title compound was investigated by the computed value of first hyperpolarizability (β0). Stability of molecule as a result of hyperconjugative interactions and electron delocalization was analyzed using NBO analysis. The HOMO and LUMO analysis is used to determine the charge transfer within the molecule. Intramolecular interactions were analyzed by AIM approach. The chemical reactivity descriptors were calculated to study the reactive sites within molecule.
Under the auspices of the U.S. Nuclear Regulatory Commission (NRC), Brookhaven National Laboratory (BNL) developed a comprehensive program to evaluate state-of-the-art methods and computer programs for seismic analysis of typical coupled nuclear power plant (NPP) systems with non-classical damping. In this program, four benchmark models of coupled building-piping/equipment systems with different damping characteristics were developed and analyzed by BNL for a suite of earthquakes. The BNL analysis was carried out by the Wilson-θ time domain integration method with the system-damping matrix computed using a synthesis formulation as presented in a companion paper [Nucl. Eng. Des. (2002)]. These benchmark problems were subsequently distributed to and analyzed by program participants applying their uniquely developed methods and computer programs. This paper is intended to offer a glimpse at the program, and provide a summary of major findings and principle conclusions with some representative results. The participant's analysis results established using complex modal time history methods showed good comparison with the BNL solutions, while the analyses produced with either complex-mode response spectrum methods or classical normal-mode response spectrum method, in general, produced more conservative results, when averaged over a suite of earthquakes. However, when coupling due to damping is significant, complex-mode response spectrum methods performed better than the classical normal-mode response spectrum method. Furthermore, as part of the program objectives, a parametric assessment is also presented in this paper, aimed at evaluation of the applicability of various analysis methods to problems with different dynamic characteristics unique to coupled NPP systems. It is believed that the findings and insights learned from this program will be useful in developing new acceptance criteria and providing guidance for future regulatory activities involving license
Stability analysis of the Gravito-Electrostatic Sheath-based solar plasma equilibrium
Karmakar, P. K.; Goutam, H. P.; Lal, M.; Dwivedi, C. B.
2016-08-01
We present approximate solutions of non-local linear perturbational analysis for discussing the stability properties of the Gravito-Electrostatic Sheath (GES)-based solar plasma equilibrium, which is indeed non-uniform on both the bounded and unbounded scales. The relevant physical variables undergoing perturbations are the self-solar gravity, electrostatic potential and plasma flow along with plasma population density. We methodologically derive linear dispersion relation for the GES fluctuations, and solve it numerically to identify and characterize the existent possible natural normal modes. Three distinct natural normal modes are identified and named as the GES-oscillator mode, GES-wave mode and usual (classical) p-mode. In the solar wind plasma, only the p-mode survives. These modes are found to be linearly unstable in wide-range of the Jeans-normalized wavenumber, k. The local plane-wave approximation marginally limits the validity or reliability of the obtained results in certain radial- and k-domains only. The phase and group velocities, time periods of these fluctuation modes are investigated. It is interesting to note that, the oscillation time periods of these modes are 3-10 min, which match exactly with those of the observed helio-seismic waves and solar surface oscillations. The proposed GES model provides a novel physical view of the waves and oscillations of the Sun from a new perspective of plasma-wall interaction physics. Due to simplified nature of the considered GES equilibrium, it is a neonatal stage to highlight its applicability in the real Sun. The proposed GES model and subsequent fluctuation analysis need further improvements to make it more realistic.
Stability analysis of the pulmonary liquid bilayer.
Halpern, David; Grotberg, James
2010-11-01
The lung consists of liquid-lined compliant airways that convey air to and from the alveoli where gas exchange takes place. Because the airways are coated with a bilayer consisting of a mucus layer on top of a periciliary fluid layer, a surface tension instability can generate flows within the bilayer and induce the formation of liquid plugs that block the passage of air. This is a problem for example with premature neonates whose lungs do not produce sufficient quantities of surfactant and suffer from respiratory distress syndrome. To study this instability a system of coupled nonlinear evolution equations are derived using lubrication theory for the thicknesses of the two liquid layers which are assumed to be Newtonian. A normal mode analysis is used to investigate the initial growth of the disturbances, and reveals how the grow rate is affected by the ratio of viscosities λ, film thicknesses η and surface tensions δ of the two layers which can change by disease. Numerical solutions of the evolution equations show that there is a critical bilayer thickness ɛc above which closure occurs, and that a more viscous and thicker layer compared to the periciliary layer closes more slowly. However, ɛcis weakly dependent on λ, η and δ. We also examine the potential impact of wall shear stress and normal stress on cell damage. This work is funded by NIH HL85156.
Isami, Shuhei; Nishimori, Hiraku; Awazu, Akinori
2015-01-01
Simple elastic network models of DNA were developed to reveal the structure-dynamics relationships for several nucleotide sequences. First, we propose a simple all-atom elastic network model of DNA that can explain the profiles of temperature factors for several crystal structures of DNA. Second, we propose a coarse-grained elastic network model of DNA, where each nucleotide is described only by one node. This model could effectively reproduce the detailed dynamics obtained with the all-atom elastic network model according to the sequence-dependent geometry. Through normal-mode analysis for the coarse-grained elastic network model, we exhaustively analyzed the dynamic features of a large number of long DNA sequences, approximately $\\sim 150$ bp in length. These analyses revealed positive correlations between the nucleosome-forming abilities and the inter-strand fluctuation strength of double-stranded DNA for several DNA sequences.
Substructure Normal Modes Selection Method for Component Mode Synthesis%模态综合的子结构主模态截断方法
李兴泉; 邓兆祥; 李传兵; 章竟成; 李英强
2014-01-01
为了减少固定界面模态综合方法中保留的子结构主模态数,分别采用频率截断和有效模态质量截断两种方法进行截断,分析两种方法的适用性,最终得到适合结构低频动态特性计算的主模态截断方法.计算结果表明:频率截断法保留的主模态不到有效质模态量截断法的1/2,采用2～3倍的最高关心频率进行主模态截断,能保证结构低频动态特性计算具有较高的精度,所保留的主模态,更能反应子结构在关心频率范围内系统振动的变形模式;有效模态质量法不能判断各子结构间主模态对系统动态特性作用的相对大小,这使小尺寸高刚度的子结构保留多余的模态,其计算效率较低.
Skákala, Jozef
2012-01-01
We analyze the largely accepted formulas for the asymptotic quasi-normal frequencies of the non-extremal Reissner-Nordström black hole, (for the electromagnetic-gravitational/scalar perturbations). We focus on the question of whether the gap in the spacing in the imaginary part of the QNM frequencies has a well defined limit as n goes to infinity and if so, what is the value of the limit. The existence and the value of this limit has a crucial importance from the point of view of the currently popular Maggiore's conjecture, which represents a way of connecting the asymptotic behavior of the quasi-normal frequencies to the black hole thermodynamics. With the help of previous results and insights we will prove that the gap in the imaginary part of the frequencies does not converge to any limit, unless one puts specific constraints on the ratio of the two surface gravities related to the two spacetime horizons. Specifically the constraints are that the ratio of the surface gravities must be rational and such that it is given by two relatively prime integers n ± whose product is an even number. If the constraints are fulfilled the limit of the sequence is still not guaranteed to exist, but if it exists its value is given as the lowest common multiplier of the two surface gravities. At the end of the paper we discuss the possible implications of our results.
Anatomy of the Binary Black Hole Recoil: A Multipolar Analysis
Schnittman, Jeremy; Buonanno, Alessandra; vanMeter, James R.; Baker, John G.; Boggs, William D.; Centrella, Joan; Kelly, Bernard J.; McWilliams, Sean T.
2007-01-01
We present a multipolar analysis of the recoil velocity computed in recent numerical simulations of binary black hole coalescence, for both unequal masses and non-zero, non-precessing spins. We show that multipole moments up to and including 1 = 4 are sufficient to accurately reproduce the final recoil velocity (= 98%) and that only a few dominant modes contribute significantly to it (2 95%). We describe how the relative amplitude, and more importantly, the relative phase, of these few modes control the way in which the recoil builds up throughout the inspiral, merger, and ring-down phases. We also find that the numerical results can be reproduced, to a high level of accuracy, by an effective Newtonian formula for the multipole moments obtained by replacing in the Newtonian formula the radial separation with an effective radius computed from the numerical data. Beyond the merger, the numerical results are reproduced by a superposition of three Kerr quasi-normal modes. Analytic formulae, obtained by expressing the multipole moments in terms of the fundamental QNMs of a Kerr BH, are able to explain the onset and amount of '.anti-kick" for each of the simulations. Lastly, we apply this multipolar analysis to understand the remarkable difference between the amplitudes of planar and non-planar kicks for equal-mass spinning black holes.
A Multiple-Scale Analysis of Evaporation Induced Marangoni Convection
Hennessy, Matthew G.
2013-04-23
This paper considers the stability of thin liquid layers of binary mixtures of a volatile (solvent) species and a nonvolatile (polymer) species. Evaporation leads to a depletion of the solvent near the liquid surface. If surface tension increases for lower solvent concentrations, sufficiently strong compositional gradients can lead to Bénard-Marangoni-type convection that is similar to the kind which is observed in films that are heated from below. The onset of the instability is investigated by a linear stability analysis. Due to evaporation, the base state is time dependent, thus leading to a nonautonomous linearized system which impedes the use of normal modes. However, the time scale for the solvent loss due to evaporation is typically long compared to the diffusive time scale, so a systematic multiple scales expansion can be sought for a finite-dimensional approximation of the linearized problem. This is determined to leading and to next order. The corrections indicate that the validity of the expansion does not depend on the magnitude of the individual eigenvalues of the linear operator, but it requires these eigenvalues to be well separated. The approximations are applied to analyze experiments by Bassou and Rharbi with polystyrene/toluene mixtures [Langmuir, 25 (2009), pp. 624-632]. © 2013 Society for Industrial and Applied Mathematics.
Compton scattering is one of major sources inducing a high background when a gamma ray spectrum is acquired from a radioactive sample. The high background spectrum deteriorates the detection sensitivity for an analysis of the nuclide of interest. To improve the detection sensitivity by the reduction of the spectrum background, a Compton suppression system (CSS) applying an anti coincidence mode was developed and has been used for a neutron activation analysis. A Compton suppression system (CSS) was implemented for an instrumental neutron activation analysis (INAA) at an NAA laboratory of the Korea Atomic Energy Research Institute (KAERI) in 2009. The CSS consists of a high purity Ge (HPGe) detector and bismuth germinate (BGO) with electronic modules. An evaluation of the performance of the CSS was carried out based on the measurement of the gamma ray emitting source and the detectable nuclides created thorough neutron activation of biological reference materials. This study was executed to evaluate the performance of the CSS for geological standard reference materials (SRMs). Four geological SRMs produced by the National Institute of Standards and Technology (NIST) in the USA were selected and irradiated using an NAA 1 irradiation hole at HANARO. Gamma ray spectra with normal mode and anti coincidence mode were acquired at the same time, and advantage factors of CSS for each nuclide detected were calculated on the basis of the signal to noise ratio
In this study, a linear stability analysis is performed in an attempt to explain the formation of the coherent structures in the narrow flow regions of complex channel flows consisting of relatively large subchannels parallel to neighbouring narrower sections. This stability analysis employs computed velocity profiles at the middle of the gaps. It introduces small amplitude perturbations of the velocity and the pressure fields and linearizes the equations of motion. A normal mode assumption is made and a search for conditions such that these specific solutions exist is done. The linearized equations are transformed into an eigenvalue problem that is solved using the spectral Tau-Chebyshev collocation method. The critical Reynolds number Rec is obtained from the thresholds for which an eigenvalue has a real part equal to zero whereas all the other eigenvalues have negative real parts. The stability analysis gave variations of the critical Reynolds number with gap size that are in qualitative agreement with published experimental stability investigations. The iso-contours of the streamwise and transverse velocities, obtained from the preferred modes solution, confirmed the presence in the gap region of counter-rotating vortices, the origin of which is the flow instability resulting from the particular velocity profile in the middle of the gap. (author)
Squeal analysis of ventilated disc brake using ansys
Ahmed Abdel-Naser, Ibrahim Ahmed, Essam Allam, Sabry Allam, Shawki Abouel-seoud
2012-01-01
Full Text Available It is well-known that automobile brakes can generate several kinds of noises. Among them is squeal, a noise in the 1-15 kHz range. It is commonly accepted that brake squeal is initiated by instability due to the friction forces, leading to self excited vibrations. To predict the onset of brake instability, a modal analysis of the prestressed structure can be performed on an improved dynamic finite element model of ventilated disc brake with friction coupling. An unsymmetric stiffness matrix is a result of the friction coupling between the brake pad and disc; this may lead to complex eigenfrequencies. The complex eigenvalue method (Unsymmetric solver used to analyse mode shapes associated with the predicted natural frequency. Creating the element of Matrix27 between the ventilated disc and pad was very important in studying the squeal of the coupled ventilated disc brake. The results demonstrated that the FEM for the coupled ventilated rotor and pad showed a good interaction between the non-linear contact and the linear modal analysis. Furthermore, the unsymmetric solver showed that the modes of the coupled disc-pad contained two types of mode. The first type was normal mode, which did not contain an imaginary part while the second type was complex mode that contained real and imaginary parts. Moreover, complex eigenvalue analysis predicted always more unstable modes than the number of squeal frequencies that really occur in the brake system. The maximum squeal index was observed at mode 16 and at frequency of 4083 Hz with instability of 480 sec-1. However; the tendency of instability (TOI for the system at contact stiffness of 1 GN/m was 59 that gave the lowest instability of the system.
Vibrational analysis of ferrocyanide complex ion based on density functional force field
Vibrational properties of ferrocyanide complex ion, [Fe(CN)6]4-, have been studied based on the force constants obtained from the density functional calculations at B3LYP/6-31G level by means of the normal mode analysis using new bond angle and linear angle internal coordinates recently developed. Vibrations of ferrocyanide were manipulated by twenty-three symmetry force constants. The angled bending deformations of C-Fe-C, the linear bending deformations of Fe-C≡N and the stretching vibrations of Fe-C have been quantitatively assigned to the calculated frequencies. The force constants in the internal coordinates employed in the modified Urey-Bradley type potential were evaluated on the density functional force field applied, and better interaction force constants in the internal coordinates have been proposed. The valence force constants in the general quadratic valence force field were also given. The stretch-stretch interaction and stretch-bending interaction constants are not sensitive to the geometrical displacement in the valence force field
This article investigates the weakly nonlinear stability theory of a thin pseudoplastic liquid film flowing down on a vertical wall. The long-wave perturbation method is employed to solve for generalized nonlinear kinematic equation with free film interface. The normal mode approach is used to compute the linear stability solution for the film flow. The method of multiple scales is then used to obtain the weak nonlinear dynamics of the film flow for stability analysis. It is shown that the necessary condition for the existence of such a solution is governed by the Ginzburg - Landau equation. The modeling results indicate that both subcritical instability and supercritical stability conditions are possible to occur in a pseudoplastic film flow system. The results also reveal that the pseudoplastic liquid film flows are less stable than Newtonian's as traveling down along the vertical wall. The degree of instability in the film flow is further intensified by decreasing the flow index n. [copyright] 2001 American Institute of Physics
IAC-1.5 - INTEGRATED ANALYSIS CAPABILITY
Vos, R. G.
1994-01-01
, object code, etc. The user can define groups of data and relations between them. A full data manipulation and query system operates with the database. The current interface modules comprise five groups: 1) Structural analysis - IAC contains a NASTRAN interface for standalone analysis or certain structural/control/thermal combinations. IAC provides enhanced structural capabilities for normal modes and static deformation analysis via special DMAP sequences. 2) Thermal analysis - IAC supports finite element and finite difference techniques for steady state or transient analysis. There are interfaces for the NASTRAN thermal analyzer, SINDA/SINFLO, and TRASYS II. 3) System dynamics - A DISCOS interface allows full use of this simulation program for either nonlinear time domain analysis or linear frequency domain analysis. 4) Control analysis - Interfaces for the ORACLS, SAMSAN, NBOD2, and INCA programs allow a wide range of control system analyses and synthesis techniques. 5) Graphics - The graphics packages PLOT and MOSAIC are included in IAC. PLOT generates vector displays of tabular data in the form of curves, charts, correlation tables, etc., while MOSAIC generates color raster displays of either tabular of array type data. Either DI3000 or PLOT-10 graphics software is required for full graphics capability. IAC is available by license for a period of 10 years to approved licensees. The licensed program product includes one complete set of supporting documentation. Additional copies of the documentation may be purchased separately. IAC is written in FORTRAN 77 and has been implemented on a DEC VAX series computer operating under VMS. IAC can be executed by multiple concurrent users in batch or interactive mode. The basic central memory requirement is approximately 750KB. IAC includes the executive system, graphics modules, a database, general utilities, and the interfaces to all analysis and controls programs described above. Source code is provided for the control
Dynamical analysis of separated boundary layer flow
Uruba, Václav
Berlin : Technische Universität Berlin, 2009. s. 1-2 ISBN N. [Nonlinear Normal Modes, Dimension Reduction and Localization in Vibrating Systems. 27.09.2009-02.10.2009, Frascati (Rome)] R&D Projects: GA ČR GA101/08/1112 Institutional research plan: CEZ:AV0Z20760514 Keywords : boundary layer * separation * dynamics Subject RIV: BK - Fluid Dynamics
Nanjundappa, C.E., E-mail: cenanju@hotmail.com [Department of Mathematics, Dr. Ambedkar Institute of Technology, Bangalore-560 056 (India); Shivakumara, I.S., E-mail: shivakumarais@gmail.com [Department of Mathematics, Bangalore University, Bangalore-560 001 (India); Prakash, H.N., E-mail: prakashahn83@gmail.com [Government Pre-University College, B H Road, Tumkur-572 102 (India)
2014-12-15
We investigate the influence of Coriolis force on the onset of thermomagnetic convection in ferrofluid saturating a porous layer in the presence of a uniform vertical magnetic field using both linear and weakly non-linear analyses. The modified Brinkman–Forchheimer-extended Darcy equation with Coriolis term has been used to describe the fluid flow. The linear theory based on normal mode method is considered to find the criteria for the onset of stationary thermomagnetic Convection and weakly non-linear analysis based on minimal representation of truncated Fourier series analysis containing only two terms has been used to find the Nusselt number Nu as functions of time. The range of thermal Rayleigh number R beyond which the bifurcation becomes subcritical increases with increasing Λ, Da{sup −1} and Ta. The global quantity of the heat transfer rate decreases by increasing the Taylor number Ta. The results obtained, during the above analyses, have been presented graphically and the effects of various parameters on heat and mass transfer have been discussed. Finally, we have drawn the steady streamlines for various parameters.
We investigate the influence of Coriolis force on the onset of thermomagnetic convection in ferrofluid saturating a porous layer in the presence of a uniform vertical magnetic field using both linear and weakly non-linear analyses. The modified Brinkman–Forchheimer-extended Darcy equation with Coriolis term has been used to describe the fluid flow. The linear theory based on normal mode method is considered to find the criteria for the onset of stationary thermomagnetic Convection and weakly non-linear analysis based on minimal representation of truncated Fourier series analysis containing only two terms has been used to find the Nusselt number Nu as functions of time. The range of thermal Rayleigh number R beyond which the bifurcation becomes subcritical increases with increasing Λ, Da−1 and Ta. The global quantity of the heat transfer rate decreases by increasing the Taylor number Ta. The results obtained, during the above analyses, have been presented graphically and the effects of various parameters on heat and mass transfer have been discussed. Finally, we have drawn the steady streamlines for various parameters
Planetary Protection Bioburden Analysis Program
Beaudet, Robert A.
2013-01-01
-time continuous service that can go quiescent after periods of inactivity. The software can process 2 GB of telemetry and deliver Level 0 science products to the end user in four hours. It provides analysis tools so the operator can manage the system and troubleshoot problems. It automates telemetry processing in order to reduce staffing costs. This work was done by Alice Stanboli, Elmain M. Martinez, and James M. McAuley of Caltech for NASA's Jet Propulsion Laboratory. For more information, contact iaoffice @jpl.nasa.gov. This software is available for commercial licensing. Please contact Dan Broderick at Daniel.F. Broderick@jpl.nasa.gov. Refer to NPO-47803. NASA Tech Briefs, September 2013 29 This rapid response computer program predicts Orbiter Wing Leading Edge (WLE) damage caused by ice or foam impact during a Space Shuttle launch (Program "IMPACT2"). The program was developed after the Columbia accident in order to assess quickly WLE damage due to ice, foam, or metal impact (if any) during a Shuttle launch. IMPACT2 simulates an impact event in a few minutes for foam impactors, and in seconds for ice and metal impactors. The damage criterion is derived from results obtained from one sophisticated commercial program, which requires hours to carry out simulations of the same impact events. The program was designed to run much faster than the commercial program with prediction of projectile threshold velocities within 10 to 15% of commercial-program values. The mathematical model involves coupling of Orbiter wing normal modes of vibration to nonlinear or linear springmass models. IMPACT2 solves nonlinear or linear impact problems using classical normal modes of vibration of a target, and nonlinear/ linear time-domain equations for the projectile. Impact loads and stresses developed in the target are computed as functions of time. This model is novel because of its speed of execution. A typical model of foam, or other projectile characterized by material nonlinearities
Benedict Thomas
2013-12-01
Full Text Available This article deals with the finite element modeling and free vibration analysis of functionally graded nanocomposite beams reinforced by randomly oriented straight single-walled carbon nanotubes (SWCNTs. Nanostructural materials can be used to alter mechanical, thermal and electrical properties of polymer-based composite materials, because of their superior properties and perfect atom arrangement. Timoshenko beam theory is used to evaluate dynamic characteristics of the beam. The Eshelby–Mori–Tanaka approach based on an equivalent fiber is used to investigate the material properties of the beam. The equations of motion are derived by using Hamilton’s principle. The finite element method is employed to discretize the model and obtain a numerical approximation of the motion equation. Different SWCNTs distributions in the thickness direction are introduced to improve fundamental natural frequency and dynamic behavior of uniform functionally graded nanocomposite beam. Results are presented in tabular and graphical forms to show the effects of various material distributions, carbon nanotube orientations, shear deformation, slenderness ratios and boundary conditions on the dynamic behavior of the beam. The first five normalized mode shapes for functionally graded carbon nanotube reinforced composite (FG-CNTRC beams with different boundary conditions and different carbon nanotubes (CNTs orientation are presented. The results show that the above mentioned effects play very important role on the dynamic behavior of the beam.
G 207-9 and LP 133-144: light curve analysis and asteroseismology of two ZZ Ceti stars
Bognár, Zs; Molnár, L; Pápics, P I; Plachy, E; Verebélyi, E; Sódor, Á
2016-01-01
G 207-9 and LP 133-144 are two rarely observed ZZ Ceti stars located in the middle and close to the blue edge of the ZZ Ceti instability domain, respectively. We aimed to observe them at least during one observing season at Konkoly Observatory with the purpose of extending the list of known pulsation modes for asteroseismic investigations and detect any significant changes in their pulsational behaviour. We determined five and three new normal modes of G 207-9 and LP 133-144, respectively. In LP 133-144, our frequency analysis also revealed that at least at three modes there are actually triplets with frequency separations of ~4 microHz. The rotational period of LP 133-144 based on the triplets is ~42 h. The preliminary asteroseismic fits of G 207-9 predict Teff=12 000 or 12 400 K and M*=0.855-0.870 MSun values for the effective temperature and mass of the star, depending on the assumptions on the spherical degree (l) values of the modes. These results are in agreement with the spectroscopic determinations. I...
Mathammal, R.; Sangeetha, K.; Sangeetha, M.; Mekala, R.; Gadheeja, S.
2016-09-01
In this study, we report a combined experimental and theoretical study on molecular structure and vibrational spectra of 3,5 di tert butyl 4 hydroxy benzoic acid. The properties of title compound have been evaluated by quantum chemical calculation (DFT) using B3LYP functional and 6-31 + G (d, p) as basis set. IR Spectra has been recorded using Fourier transform infrared spectroscopy (FT-IR) in the region 4000-400 cm-1. The vibrational assignment of the calculated normal modes has been made on the basis set. The isotropic chemical shifts computed by 13C and 1H NMR (Nuclear Magnetic Resonance) analyses also show good agreement with experimental observations. The theoretical UV-Vis spectrum of the compound are used to study the visible absorption maxima (λ max). The structure activity relationship have been interpreted by mapping electrostatic potential surface (MEP), which is valuable information for the quality control of medicines and drug receptor interactions. The Mullikan charges, HOMO (Highest Occupied Molecular Orbital) - LUMO (Lowest Unoccupied Molecular Orbital) energy are analyzed. HOMO-LUMO energy gap and other related molecular properties are also calculated. The Natural Bond Orbital (NBO) analysis is carried out to investigate the various intra and inter molecular interactions of molecular system. The Non-linear optical properties such as dipole moment (μ), polarizability (αtot) and molecular first order hyperpolarizability (β) of the title compound are computed with B3LYP/6-31 + G (d,p) level of theory.
Infrared reflectance and ellipsometry measurements are applied in order to study the influence of Mg-doping on the properties of hexagonal InN films. Reflectance spectrum characteristics reveal the large effective mass and large plasmon damping rate just in the region where net acceptors have been observed by electrolyte capacitance-voltage technique. The numerical spectrum analysis accounting for the modulation of the normal mode energies of longitudinal optical phonon-plasmon coupling (LOPC) by the large hole scattering rate yields the hole density of (0.1-1.2) x 1019 cm-3 and optical mobility of 25-70 cm2/Vs for the direction vertical to the c axis. The properties of the bulk-like part of the films are determined by the optical techniques. Infrared ellipsometry on the study of anisotropy of LOPC mode broadening indicates that threading dislocations or columnar grain boundaries cause the significantly larger scattering rate for holes vibrating along the c axis than those vibrating vertical to the c axis. (copyright 2009 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Abkari, A.; Chaabane, I.; Guidara, K.
2016-07-01
The organic-inorganic salt, bis(4-acetylanilinium) tetrachlorocuprate(II), was synthesized and characterized by means of FT-IR (4000-400 cm-1) and Raman (3500-50 cm-1) in solid phase. The structure of [C8H10NO]2CuCl4 compound which was optimized by density functional theory (DFT) using B3LYP method showed that the calculated values obtained by B3LYP with LanL2DZ and 6311G+(d,p) basis sets are in better agreement with the experimental data. The computed vibrational frequencies were scaled by different scale factors to yield a good agreement with the experimental vibrational frequencies. The latter have been discussed on the basis of quantum chemical DFT calculations using the B3LYP/6311G+(d,p) and B3LYP/LanL2DZ method approach in gas phase. Besides, the effects due to the substitutions and the intermolecular interactions were investigated. The comparative analysis of the Raman spectra of the title compound with that of the free ligand was also discussed. The geometries and normal modes of the vibrations obtained from B3LYP/6311G+(d,p) calculation are found to be in good agreement with the experimentally observed data. The complete vibrational assignments and analysis of the observed fundamental bands of molecule were carried out.
Benzon, K. B.; Varghese, Hema Tresa; Panicker, C. Yohannan; Pradhan, Kiran; Tiwary, Bipransh Kumar; Nanda, Ashis Kumar; Alsenoy, C. Van
2015-07-01
In this work, the vibrational spectral analysis was carried out using FT-IR and FT-Raman spectroscopy of 2-(4-hydroxyphenyl)-4,5-dimethyl-1H-imidazole 3-oxide. The computations were performed at DFT levels of theory to get the optimized geometry and vibrational frequencies of the normal modes of the title compound using Gaussian09 software. The complete vibrational assignments of frequencies were made on the basis of potential energy distribution. The calculated HOMO and LUMO energies show the chemical activity of the molecule. The stability of the molecule arising from hyper-conjugative interaction and charge delocalization has been analyzed using NBO analysis. The hyperpolarizability values are reported and the first hyperpolarizability of the title compound is 19.61 times that of standard NLO material urea. From the MEP plot, the negative charge covers the nitro group and the positive region is over the hydroxyl group and N-H part of the imidazole ring. The calculated 1H NMR results are in good agreement with experimental data. Molecular docking study is also reported.
Bejugam, Pruthvi Raj; Singh, Shailza
2016-01-01
In the modern era of post genomics and transcriptomics, non-coding RNAs and non-coding regions of many RNAs are a big puzzle when we try deciphering their role in specific gene function. Gene function assessment is a main task wherein high throughput technologies provide an impressive body of data that enables the design of hypotheses linking genes to phenotypes. Gene knockdown technologies and RNA-dependent gene silencing are the most frequent approaches to assess the role of key effectors in a particular scenario. Ribozymes are effective modulators of gene expression because of their simple structure, site-specific cleavage activity, and catalytic potential. In our study, after an extensive transcriptomic search of Leishmania major transcriptome we found a Putative ATP dependent DNA helicase (Lmjf_09_0590) 3' UTR which has a structural signature similar to well-known HDV hammerhead ribozyme, even though they have variable sequence motifs. Henceforth, to determine their structural stability and sustainability we analyzed our predicted structural model of this 3'UTR with a 30ns MD simulation, further confirmed with 100ns MD simulation in presence of 5mM MgCl2 ionic environment. In this environment, structural stability was significantly improved by bonded interactions between a RNA backbone and Mg2+ ions. These predictions were further validated in silico using RNA normal mode analysis and anisotropic network modelling (ANM) studies. The study may be significantly imparted to know the functional importance of many such 3'UTRs to predict their role in a mechanistic manner. PMID:26901858
Pruthvi Raj Bejugam
Full Text Available In the modern era of post genomics and transcriptomics, non-coding RNAs and non-coding regions of many RNAs are a big puzzle when we try deciphering their role in specific gene function. Gene function assessment is a main task wherein high throughput technologies provide an impressive body of data that enables the design of hypotheses linking genes to phenotypes. Gene knockdown technologies and RNA-dependent gene silencing are the most frequent approaches to assess the role of key effectors in a particular scenario. Ribozymes are effective modulators of gene expression because of their simple structure, site-specific cleavage activity, and catalytic potential. In our study, after an extensive transcriptomic search of Leishmania major transcriptome we found a Putative ATP dependent DNA helicase (Lmjf_09_0590 3' UTR which has a structural signature similar to well-known HDV hammerhead ribozyme, even though they have variable sequence motifs. Henceforth, to determine their structural stability and sustainability we analyzed our predicted structural model of this 3'UTR with a 30ns MD simulation, further confirmed with 100ns MD simulation in presence of 5mM MgCl2 ionic environment. In this environment, structural stability was significantly improved by bonded interactions between a RNA backbone and Mg2+ ions. These predictions were further validated in silico using RNA normal mode analysis and anisotropic network modelling (ANM studies. The study may be significantly imparted to know the functional importance of many such 3'UTRs to predict their role in a mechanistic manner.
Decision analysis multicriteria analysis
The ALARA procedure covers a wide range of decisions from the simplest to the most complex one. For the simplest one the engineering judgement is generally enough and the use of a decision aiding technique is therefore not necessary. For some decisions the comparison of the available protection option may be performed from two or a few criteria (or attributes) (protection cost, collective dose,...) and the use of rather simple decision aiding techniques, like the Cost Effectiveness Analysis or the Cost Benefit Analysis, is quite enough. For the more complex decisions, involving numerous criteria or for decisions involving large uncertainties or qualitative judgement the use of these techniques, even the extended cost benefit analysis, is not recommended and appropriate techniques like multi-attribute decision aiding techniques are more relevant. There is a lot of such particular techniques and it is not possible to present all of them. Therefore only two broad categories of multi-attribute decision aiding techniques will be presented here: decision analysis and the outranking analysis
Maheswari, R.; Manjula, J.
2016-07-01
(E)-4-methoxy-N‧-(4-methylbenzylidene)benzohydrazide (4MN'MBH) a novel, organic, hydrazone Schiff base compound was synthesized and its structure was characterized by Fourier Transform Infrared (4000-400 cm-1), Fourier Transform Raman (3500-50 cm-1), Ultraviolet-Visible (200-800 nm) and 1H and 13C NMR spectroscopic analysis. Optimized molecular structure, vibrational frequencies and corresponding vibrational assignments regarding 4MN'MBH has become screened tentatively as well as hypothetically utilizing Gaussian09Wprogram package. Potential energy distributions of the normal modes of vibrations connected with vibrations are generally accomplished by applying VEDA program. Natural Bonding Orbital (NBO) assessment was completed with a reason to clarify charge transfer or conjugative interaction, the intra-molecular-hybridization and delocalization of electron density within the molecule. Electronic transitions were studied employing UV-Visible spectrum and the observed values were compared with theoretical values. 1H and13C NMR spectral assessment had been made with choosing structure property relationship by chemical shifts along with magnetic shielding effects of title compound. The first order hyperpolarizability (β0) and related properties (β, α0 and Δα) of 4MN'MBH were calculated. The computed first order hyperpolarizability commensurate with the documented worth of very similar structure and could be an interesting thing for more experiments on non linear optics. Molecular docking study has been performed by in silico method to analysis their antituberculosis aspects against Enoyl acyl carrier protein reductase (Mycobacterium tuberculosis InhA) protein.
Compton suppression naa in the analysis of food and beverages
Applicability and performance of Compton suppression method in the analysis of food and beverages was re-established in this study. Using ''1''3''7Cs and ''6''0Co point sources Compton Suppression Factors (SF), Compton Reduction Factors (RF), Peak-to-Compton ratio (P/C), Compton Plateau (Cpl), and Compton Edge (Ce) were determined for each of the two sources. The natural background reduction factors in the anticoincidence mode compared to the normal mode were evaluated. The reported R.F. values of the various Compton spectrometers for ''6''0Co source at energy 50-210 keV (backscattering region), 600 keV (Compton edge corresponding to 1173.2 keV gamma-ray) and 1110 keV (Compton edge corresponding to 1332.5 keV gamma-ray) were compared with that of the present work. Similarly the S.F. values of the spectrometers for ''1''3''7Cs source were compared at the backscattered energy region (S.F.b = 191-210 keV), Compton Plateau (S.F.pl = 350-370 keV), and Compton Edge (S.F.e = 471-470 keV) and all were found to follow a similar trend. We also compared peak reduction ratios for the two cobalt energies (1173.2 and 1332.5) with the ones reported in literature and two results agree well. Applicability of the method to food and beverages was put to test for twenty one major, minor, and trace elements (Ba, Sr, I, Br, Cu, V, Mg, Na, Cl, Mn, Ca, Sn,K, Cd, Zn, As, Sb, Ni, Cs, Fe, and Co) commonly found in food, milk, tea and tobacco. The elements were assayed using five National Institute for Standards and Technology (NIST) certified reference materials (Non-fat powdered milk, Apple leaves, Tomato leaves, and Citrus leaves). The results obtained shows good agreement with NIST certified values, indicating that the method is suitable for simultaneous determination of micro-nutrients, macro-nutrients and heavy elements in food and beverages without undue interference problems
Sreekantamurthy, Tham; Gaspar, James L.; Mann, Troy; Behun, Vaughn; Pearson, James C., Jr.; Scarborough, Stephen
2007-01-01
Ultra-light weight and ultra-thin membrane inflatable antenna concepts are fast evolving to become the state-of-the-art antenna concepts for deep-space applications. NASA Langley Research Center has been involved in the structural dynamics research on antenna structures. One of the goals of the research is to develop structural analysis methodology for prediction of the static and dynamic response characteristics of the inflatable antenna concepts. This research is focused on the computational studies to use nonlinear large deformation finite element analysis to characterize the ultra-thin membrane responses of the antennas. Recently, structural analyses have been performed on a few parabolic reflector antennas of varying size and shape, which are referred in the paper as 0.3 meters subscale, 2 meters half-scale, and 4 meters full-scale antenna. The various aspects studied included nonlinear analysis methodology and solution techniques, ways to speed convergence in iterative methods, the sensitivities of responses with respect to structural loads, such as inflation pressure, gravity, and pretension loads in the ground and in-space conditions, and the ultra-thin membrane wrinkling characteristics. Several such intrinsic aspects studied have provided valuable insight into evaluation of structural characteristics of such antennas. While analyzing these structural characteristics, a quick study was also made to assess the applicability of dynamics scaling of the half-scale antenna. This paper presents the details of the nonlinear structural analysis results, and discusses the insight gained from the studies on the various intrinsic aspects of the analysis methodology. The predicted reflector surface characteristics of the three inflatable ultra-thin membrane parabolic reflector antenna concepts are presented as easily observable displacement fringe patterns with associated maximum values, and normal mode shapes and associated frequencies. Wrinkling patterns are
Fast and anisotropic flexibility-rigidity index for protein flexibility and fluctuation analysis
Opron, Kristopher [Department of Biochemistry and Molecular Biology, Michigan State University, Michigan 48824 (United States); Xia, Kelin [Department of Mathematics, Michigan State University, Michigan 48824 (United States); Wei, Guo-Wei, E-mail: wei@math.msu.edu [Department of Biochemistry and Molecular Biology, Michigan State University, Michigan 48824 (United States); Department of Mathematics, Michigan State University, Michigan 48824 (United States); Department of Electrical and Computer Engineering, Michigan State University, Michigan 48824 (United States)
2014-06-21
, normal mode analysis and Gaussian network model (GNM). The accuracy of the FRI method is tested using four sets of proteins, three sets of relatively small-, medium-, and large-sized structures and an extended set of 365 proteins. A fifth set of proteins is used to compare the efficiency of the FRI, fFRI, aFRI, and GNM methods. Intensive validation and comparison indicate that the FRI, particularly the fFRI, is orders of magnitude more efficient and about 10% more accurate overall than some of the most popular methods in the field. The proposed fFRI is able to predict B-factors for α-carbons of the HIV virus capsid (313 236 residues) in less than 30 seconds on a single processor using only one core. Finally, we demonstrate the application of FRI and aFRI to protein domain analysis.
Fast and anisotropic flexibility-rigidity index for protein flexibility and fluctuation analysis
Protein structural fluctuation, typically measured by Debye-Waller factors, or B-factors, is a manifestation of protein flexibility, which strongly correlates to protein function. The flexibility-rigidity index (FRI) is a newly proposed method for the construction of atomic rigidity functions required in the theory of continuum elasticity with atomic rigidity, which is a new multiscale formalism for describing excessively large biomolecular systems. The FRI method analyzes protein rigidity and flexibility and is capable of predicting protein B-factors without resorting to matrix diagonalization. A fundamental assumption used in the FRI is that protein structures are uniquely determined by various internal and external interactions, while the protein functions, such as stability and flexibility, are solely determined by the structure. As such, one can predict protein flexibility without resorting to the protein interaction Hamiltonian. Consequently, bypassing the matrix diagonalization, the original FRI has a computational complexity of O(N2). This work introduces a fast FRI (fFRI) algorithm for the flexibility analysis of large macromolecules. The proposed fFRI further reduces the computational complexity to O(N). Additionally, we propose anisotropic FRI (aFRI) algorithms for the analysis of protein collective dynamics. The aFRI algorithms permit adaptive Hessian matrices, from a completely global 3N × 3N matrix to completely local 3 × 3 matrices. These 3 × 3 matrices, despite being calculated locally, also contain non-local correlation information. Eigenvectors obtained from the proposed aFRI algorithms are able to demonstrate collective motions. Moreover, we investigate the performance of FRI by employing four families of radial basis correlation functions. Both parameter optimized and parameter-free FRI methods are explored. Furthermore, we compare the accuracy and efficiency of FRI with some established approaches to flexibility analysis, namely, normal mode
Banks, J. W.; Henshaw, W. D.; Schwendeman, D. W.
2014-07-01
Stable partitioned algorithms for fluid-structure interaction (FSI) problems are developed and analyzed in this two-part paper. Part I describes an algorithm for incompressible flow coupled with compressible elastic solids, while Part II discusses an algorithm for incompressible flow coupled with structural shells. Importantly, these new added-mass partitioned (AMP) schemes are stable and retain full accuracy with no sub-iterations per time step, even in the presence of strong added-mass effects (e.g. for light solids). The numerical approach described here for bulk compressible solids extends the scheme of Banks et al. [1,2] for inviscid compressible flow, and uses Robin (mixed) boundary conditions with the fluid and solid solvers at the interface. The basic AMP Robin conditions, involving a linear combination of velocity and stress, are determined from the outgoing solid characteristic relation normal to the fluid-solid interface combined with the matching conditions on the velocity and traction. Two alternative forms of the AMP conditions are then derived depending on whether the fluid equations are advanced with a fractional-step method or not. The stability and accuracy of the AMP algorithm is evaluated for linearized FSI model problems; the full nonlinear case being left for future consideration. A normal mode analysis is performed to show that the new AMP algorithm is stable for any ratio of the solid and fluid densities, including the case of very light solids when added-mass effects are large. In contrast, it is shown that a traditional partitioned algorithm involving a Dirichlet-Neumann coupling for the same FSI problem is formally unconditionally unstable for any ratio of densities. Exact traveling wave solutions are derived for the FSI model problems, and these solutions are used to verify the stability and accuracy of the corresponding numerical results obtained from the AMP algorithm for the cases of light, medium and heavy solids.
This textbook deals with instrumental analysis, which consists of nine chapters. It has Introduction of analysis chemistry, the process of analysis and types and form of the analysis, Electrochemistry on basic theory, potentiometry and conductometry, electromagnetic radiant rays and optical components on introduction and application, Ultraviolet rays and Visible spectrophotometry, Atomic absorption spectrophotometry on introduction, flame emission spectrometry and plasma emission spectrometry. The others like infrared spectrophotometry, X-rays spectrophotometry and mass spectrometry, chromatography and the other instrumental analysis like radiochemistry.
Chang Jan-Gowth
2011-10-01
Full Text Available Abstract Background Multiple acyl-coenzyme A dehydrogenase deficiency (MADD is an autosomal recessive disease caused by the defects in the mitochondrial electron transfer system and the metabolism of fatty acids. Recently, mutations in electron transfer flavoprotein dehydrogenase (ETFDH gene, encoding electron transfer flavoprotein:ubiquinone oxidoreductase (ETF:QO have been reported to be the major causes of riboflavin-responsive MADD. To date, no studies have been performed to explore the functional impact of these mutations or their mechanism of disrupting enzyme activity. Results High resolution melting (HRM analysis and sequencing of the entire ETFDH gene revealed a novel mutation (p.Phe128Ser and the hotspot mutation (p.Ala84Thr from a patient with MADD. According to the predicted 3D structure of ETF:QO, the two mutations are located within the flavin adenine dinucleotide (FAD binding domain; however, the two residues do not have direct interactions with the FAD ligand. Using molecular dynamics (MD simulations and normal mode analysis (NMA, we found that the p.Ala84Thr and p.Phe128Ser mutations are most likely to alter the protein structure near the FAD binding site as well as disrupt the stability of the FAD binding required for the activation of ETF:QO. Intriguingly, NMA revealed that several reported disease-causing mutations in the ETF:QO protein show highly correlated motions with the FAD-binding site. Conclusions Based on the present findings, we conclude that the changes made to the amino acids in ETF:QO are likely to influence the FAD-binding stability.
Wang, L.; Chen, C.; Du, J.; Wang, Q.
2011-12-01
The Earth's free oscillations always happen after strong earthquakes. Observations and studies on the Earth's free oscillations will provide an important reference for understanding the Earth's internal structure and anisotropic characters. As the Earth's spherical oscillations always induce the Earth surface's vertical displacement which can be observed by gravimeter consecutively, the correlation signal of the Earth's free oscillations will be obtained. The earthquake (Mw=9.0) happened in the 130km (38.322°N, 142.369°E) of the Pacific sea area which located at the east of Sendai City at GMT time 05:46:23, on March 11th, 2011, has been the biggest earthquake in Japan so far, which has caused the Pacific Ocean not only tsunami disaster but also induced the Earth's free oscillations worldwide. After strong earthquakes, the Earth oscillates with spheroidal and toroidal modes. The former cause gravity changes which can be detected with sensitive instruments. For this purpose, we used continuous gravity measurements with LaCoste&Romberg Earth Tide spring gravimeter (gPhone) to make continuous gravity measurement in China University of Geosciences, Wuhan. The Microg-LaCoste gPhone is a portable Earth tide gravimeter equipped with a 0.1 μGal resolution feedback. The core sensor is the patented LaCoste & Romberg (LR) zero-length spring suspension system. We analyzed on the co-seismic corresponding signals of the observed gravity data after the earthquake (Mw=9.0) happened in the east of Honshu, Japan on 3.11. Then we provided the observed Earth's free oscillations results recorded by #94 gPhone which aroused by this strong earthquake. Spectral analysis of detided and depressured records showed significant peaks in normal modes within frequency range. These peaks are above noise level and they are in good accordance with seismic theories. Here, we show some examples of normal modes registration after great earthquakes, such as: We estimated 43 Earth's free oscillation
Dynamic thrust analysis for pressurizer safety and relief valve discharge with water seal
Dynamic shock loadings and fast temperature transients are two distinct areas of concern for the design of the pressurizer safety and relief valve (PSARV) discharge piping system for pressurizer water reactors. The safety/relief system, located on the top of the pressurizer, provides overpressure protection for the reactor coolant system. For some facilities, a cold water seal is established directly upstream of the valve to prevent an interface between pressurizer steam and the valve seat. This water seal practically eliminates the possibility of valve leakage. While this arrangement maximizes the plant availability, its operation could impose extremely severe hydraulic shock loads on the piping and supports. To reduce the severity of these shock loads, proper design considerations must be used in establishing the piping layout and the supporting mechanism for the system. There are two distinct steps in this dynamic piping stress analysis - the development of time-history hydraulic forces generated upon actuation of the safety and relief valves, and a dynamic structural analysis of the piping system to determine the deformation and load responses due to the application of these forces. The dynamic thrust analysis is performed on a time-history basis. A mathematical model consisting of node points and lumped masses connected by piping elements is developed. Supports are represented by linear and/or non-linear springs which define the restraint characteristics of supports. The time-history hydraulic forces are applied to the lumped mass points of the piping system. The dynamic solution is obtained by using a modified predictor-corrector integration technique and normal mode theory. The system is composed of Class 1, Class 2 and Non-nuclear Safety Class piping. The piping is designed and evaluated in accordance with the guidelines set forth in the ASME Boiler and Pressure Vessel Code, Section III, subsections NB, NC and ND. The operability and structural integrity of
... page: //medlineplus.gov/ency/article/003741.htm Sensitivity analysis To use the sharing features on this page, please enable JavaScript. Sensitivity analysis determines the effectiveness of antibiotics against microorganisms (germs) ...
Gionis, Aristides
2013-01-01
The objective of this report is to highlight opportunities for enhancing global research data infrastructures from the point of view of data analysis. We discuss various directions and data-analysis functionalities for supporting such infrastructures.
Cerebrospinal fluid analysis ... Analysis of CSF can help detect certain conditions and diseases. All of the following can be, but ... An abnormal CSF analysis result may be due to many different causes, ... Encephalitis (such as West Nile and Eastern Equine) Hepatic ...
Merzel, F; Johnson, M R; Fontaine-Vive, Fabien; Johnson, Mark R.; Merzel, Franci
2006-01-01
Computational tools for normal mode analysis, which are widely used in physics and materials science problems, are designed here in a single package called NMscatt (Normal Modes & scattering) that allows arbitrarily large systems to be handled. The package allows inelastic neutron and X-ray scattering observables to be calculated, allowing comparison with experimental data produced at large scale facilities. Various simplification schemes are presented for analysing displacement vectors, which are otherwise too complicated to understand in very large systems.
Dynamics, stability analysis and quantization of -Fermi–Pasta–Ulam lattice
Rupali L Sonone; Sudhir R Jain
2014-12-01
We study the well-known one-dimensional problem of particles with nonlinear interaction. The -Fermi–Pasta–Ulam model is the special case of quadratic and quartic interaction potential among nearest neighbours. We enumerate and classify the simple periodic orbits for this system and find the stability zones, employing Floquet theory. We quantize the nonlinear normal modes and construct a wavefunction for what we believe is a primitive nonlinear analogue of a `phonon’.
A two-layer model for linear stability analysis of shelf-slope currents.
Teigen, Sigurd Henrik
2011-01-01
A method for obtaining the normal mode solution of a linear two-layer system over sloping topography has been derived and implemented, providing a basic tool for analysing the disper- sion relation and modal structure of stable and unstable baroclinic shelf waves. Model results are compared with analytical solutions for a step-shelf profile with no background flow and a linearly sloping channel with flow in both layers. A case study for the West Spitsbergen Shelf topography is also pre...
Kantorovich, L V
1982-01-01
Functional Analysis examines trends in functional analysis as a mathematical discipline and the ever-increasing role played by its techniques in applications. The theory of topological vector spaces is emphasized, along with the applications of functional analysis to applied analysis. Some topics of functional analysis connected with applications to mathematical economics and control theory are also discussed. Comprised of 18 chapters, this book begins with an introduction to the elements of the theory of topological spaces, the theory of metric spaces, and the theory of abstract measure space
The neutron activation analysis, which appears to be in limits for further advance, is the most suitable for providing information on the principal as well as the microcomponents in any sample of solid form. Then, instrumental activation analysis is capable of determination of far many elements in various samples. Principally on the neutron activation analysis, the following are described in literature survey from 1982 to middle 1984: bibliography, review, data collection, etc.; problems in spectral analysis and measurement; activation analysis with neutrons; charged particle and photo-nucleus reactions; chemical separation, isotopic dilution activation analysis; molecular activation analysis; standard materials; life and its relation samples; environmental, food, court trial and archaeological samples; space and earth sciences. (Mori, K.)
Vargas-Magaña, Rosa; Panayotaros, Panayotis
2015-11-01
We study the problem of wave propagation in a long-wave asymptotic regime over variable bottom of an ideal irrotational fluid in the framework of the Hamiltonian formulation in which the non-local Dirichlet-Neumann (DtN) operator appears explicitly in the Hamiltonian. We propose a non-local Hamiltonian model for bidirectional wave propagation in shallow water that involves pseudodifferential operators that approximate the DtN operator for variable depth. These models generalize the Boussinesq system as they include the exact dispersion relation in the case of constant depth. We present results for the normal modes and eigenfrequencies of the linearized problem. We see that variable topography introduces effects such as steepening of normal modes with increasing variation of depth, as well as amplitude modulation of the normal modes in certain wavelength ranges. Numerical integration shows that the constant depth nonlocal Boussinesq model with quadratic nonlinearity can capture the evolution obtained with higher order approximations of the DtN operator. In the case of variable depth we observe certain oscillations in width of the crest and also some interesting textures in the evolution of wave crests during the passage from obstacles.
Raman spectroscopic analysis of isomers of biliverdin dimethyl ester.
Matysik, J; Hildebrandt, P; Smit, K; Mark, F; Gärtner, W; Braslavsky, S E; Schaffner, K; Schrader, B
1997-06-01
The constitutional isomers of biliverdin dimethyl ester, IX alpha and XIII alpha, were studied by resonance Raman spectroscopy. The far-reaching spectral similarities suggest that despite the different substitution patterns, the compositions of the normal modes are closely related. This conclusion does not hold only for the parent state (ZZZ, sss configuration) but also for the configurational isomers which were obtained upon double-bond photoisomerization. Based on a comparison of the resonance Raman spectra, a EZZ configuration is proposed for one of the two photoisomers of biliverdin dimethyl ester IX alpha, while a ZZE, ssa configuration has been assigned previously to the second isomer. PMID:9226559
Zero, Normal and Super-radiant Modes for Scalar and Spinor Fields in Kerr-anti de Sitter Spacetime
Kenmoku, Masakatsu; Shigemoto, Kazuyasu; Yoon, Jong Hyuk
2016-01-01
Zero and normal modes for scalar and spinor fields in Kerr-anti de Sitter spacetime are studied as bound state problem with Dirichlet and Neumann boundary conditions. Zero mode is defined as the momentum near the horizon to be zero: $p_{\\rm H}=\\omega-\\Omega_{\\rm H}m=0$, and is shown not to exist as physical state for both scalar and spinor fields. Physical normal modes satisfy the spectrum condition $p_{\\rm H}>0$ as a result of non-existence of zero mode and the analyticity with respect to rotation parameter $a$ of Kerr-anti de Sitter black hole. Comments on the super-radiant modes and the thermodynamics of black hole are given in relation to the spectrum condition for normal modes. Preliminary numerical analysis on normal modes is presented.
Bartuňková, Alena
2008-01-01
The objective of this Bachelor thesis is to carry out a strategic analysis of a Czech owned limited company, Česky národní podnik s.r.o. This company sells traditional Czech products and manufactures cosmetics and body care products. The first part of the thesis provides theoretical background and methodology that are used later for the strategic analysis of the company. The theory outlined in this paper is based on the analysis of external and internal factors. Firstly the PEST analysis has ...
Chládek, Vítězslav
2012-01-01
The objective of this Bachelor thesis is to carry out a strategic analysis of a Czech owned limited company, Česky národní podnik s.r.o. This company sells traditional Czech products and manufactures cosmetics and body care products. The first part of the thesis provides theoretical background and methodology that are used later for the strategic analysis of the company. The theory outlined in this paper is based on the analysis of external and internal factors. Firstly the PEST analysis has ...
Li, L.; Braat, L.C.; Lei, G.; Arets, E.J.M.M.; Liu, J.; Jiang, L.; Fan, Z.; Liu, W.; He, H.; Sun, X.
2014-01-01
This chapter presents the results of the scenario analysis of China’s ecosystems focusing on forest, grassland, and wetland ecosystems. The analysis was undertaken using Conversion of Land Use Change and its Effects (CLUE) modeling and an ecosystem service matrix (as explained below) complemented by
Lanczos, Cornelius
2010-01-01
Basic text for graduate and advanced undergraduate deals with search for roots of algebraic equations encountered in vibration and flutter problems and in those of static and dynamic stability. Other topics devoted to matrices and eigenvalue problems, large-scale linear systems, harmonic analysis and data analysis, more.
Rigid Body Modes Influence On Microvibration Analysis-Application To Swarm
Laduree, G.; Fransen, S.; Baldesi, G.; Pflieger, I.
2012-07-01
Microvibrations are defined as low level mechanical disturbances affecting payload performance, generated by mobile parts or mechanism operating on-board the spacecraft, like momentum or reaction wheels, pointing mechanism, cryo-coolers or thrusters. The disturbances caused by these sources are transmitted through the spacecraft structure and excite modes of that structure or elements of the payload impacting its performance (e.g. Line of sight rotations inducing some image quality degradation). The dynamic interaction between these three elements (noise source, spacecraft structure and sensitive receiver) makes the microvibration prediction a delicate problem. Microvibration sources are generally of concern in the frequency range from a few Hz to 1000 Hz. However, in some specific cases, high stability at lower frequencies might be requested. This is the case of the SWARM mission, whose objectives are to provide the best ever survey of the geomagnetic field and its temporal evolution as well as supplementary information for studying the interaction of the magnetic field with other physical quantities describing the Earth system (e.g. ocean circulation). Among its instruments, SWARM is embarking a very sensitive 6-axis accelerometer in the low frequency range (10-8 m/s2 or rad/s2 between 10-4 and 0.1 Hz) located at its Centre of Gravity and an Absolute Scalar Magnetometer located at the tip of a boom far from the spacecraft body. The ASM performs its measurements by rotating an alternative magnetic field around its main axis thanks to a piezo-electric motor. This repeated disturbance might generate some pollution of the accelerometer science data. The objective of this work is to focus on the interaction of the rigid body mode calculation method with the elastic contribution of the normal modes excited by the noise source frequency content. It has indeed been reported in the past that NASTRAN Lanczos rigid body modes may lead to inaccurate rigid-body accelerations
We undertook a study programme at the end of 1991. To start with, we performed some exploratory studies aimed at learning some preliminary lessons on this type of analysis: Assessment of the interest of probabilistic incident analysis; possibility of using PSA scenarios; skills and resources required. At the same time, EPN created a working group whose assignment was to define a new approach for analysis of incidents on NPPs. This working group gave thought to both aspects of Operating Feedback that EPN wished to improve: Analysis of significant incidents; analysis of potential consequences. We took part in the work of this group, and for the second aspects, we proposed a method based on an adaptation of the event-tree method in order to establish a link between existing PSA models and actual incidents. Since PSA provides an exhaustive database of accident scenarios applicable to the two most common types of units in France, they are obviously of interest for this sort of analysis. With this method we performed some incident analyses, and at the same time explores some methods employed abroad, particularly ASP (Accident Sequence Precursor, a method used by the NRC). Early in 1994 EDF began a systematic analysis programme. The first, transient phase will set up methods and an organizational structure. 7 figs
Factor Analysis via Components Analysis
Bentler, Peter M.; de Leeuw, Jan
2011-01-01
When the factor analysis model holds, component loadings are linear combinations of factor loadings, and vice versa. This interrelation permits us to define new optimization criteria and estimation methods for exploratory factor analysis. Although this article is primarily conceptual in nature, an illustrative example and a small simulation show…